Algebra Solver With Steps

What problems can the algebra solver handle?

The solver covers most of what you meet in Algebra 1 and Algebra 2. On the equation side, that means linear, quadratic and polynomial equations up to degree 6, plus inequalities, absolute value equations and systems of up to 4 linear equations. On the expression side, it factors, simplifies, expands and divides polynomials, and it does fraction and radical arithmetic.

The menu next to the input box sets the operation. Solve is the default and covers most of the table: it solves equations, and if you give it an expression with no equals sign, it simplifies it. For the other rows, pick Solve system, Find zeros, Factor, Expand, Calculate or Simplify radical. Each row below is a real problem you can paste in, and the answer column is what comes back.

Every type in the table also has its own page with a guide written for that topic. The quadratic equation solver, the system of equations calculator and the factoring calculator are good places to start. The full list sits on the calculators page.

Can you use it as a free math solver?

Yes, for algebra and the arithmetic around it. The same box that solves 2(x + 3) = 14 also works out calculations such as sqrt(50) + sqrt(8), which gives 7√2, or sin(30), which gives 1/2. It also solves equations with x in a denominator, square root equations like sqrt(x + 3) = x − 3, and exponent equations like 2^x = 8. Every answer still comes with the steps and a check.

If you only need a number, the scientific calculator is quicker. It works like a handheld one, with log, ln, x², xʸ, sin and cos keys, exact fractions and a history of results. Its Show steps button sends the problem back here when you want the working.

This math solver doesn't do calculus, geometry proofs or statistics. For those topics the solver says it can't help instead of guessing.

How does the solver work out 2(x + 3) = 14?

It clears the parentheses, moves the constant, divides, and then checks. Those are the same four moves a teacher would expect on paper, in the same order.

Every step in the solver has a title, the line before and after, and a one-sentence reason. For this problem the second step reads "Subtract 6 from both sides" and shows 2x + 6 − 6 = 14 − 6. Its note says that subtracting the same number on both sides keeps the equation balanced.

That reason line is the part worth reading. Teachers often ask why a move is allowed. The answer is usually one of a handful of rules: the same operation on both sides, the distributive property, or combining like terms. Seeing those rules next to real numbers makes them easier to remember.

If you only need the answer, skim to the bottom. If you're stuck on one line of your own work, find the matching line in the solver and compare the two.

How does it solve quadratic and higher-degree equations?

For a quadratic, it writes the equation in standard form, works out the discriminant, and applies the quadratic formula. For cubics and beyond, it lists the possible rational roots, tests them, and divides each root out with synthetic division.

Take x² − 5x − 14 = 0. Here a = 1, b = −5 and c = −14, so the discriminant is (−5)² − 4(1)(−14) = 81. The formula gives x = (5 ± 9)/2, which is x = 7 or x = −2.

For x³ − 6x² + 11x − 6, the candidates are ±1, ±2, ±3 and ±6. Testing them shows 1, 2 and 3 all give zero, and the synthetic division steps confirm each one. The zeros calculator and the synthetic division calculator show these steps on their own pages.

Some quadratics have no real answer. x² + 2x + 5 = 0 has a negative discriminant, so by default you'll see "No real solution". If your class works with complex numbers, set the Number domain option to Complex numbers and the same equation gives x = −1 ± 2i.

How does it solve a system of equations?

It uses elimination: it scales and subtracts equations until each one has a single variable left. Choose Solve system and type the equations on one line with a comma between them.

Up to 4 equations with up to 4 unknowns work the same way. If the equations contradict each other, as with x + 2y = 5 and 2x + 4y = 7, you'll see "No solution" instead of a made-up answer. For two-variable systems the system of equations calculator also draws both lines, so you can see where they cross.

The opposite case shows up too. When one equation is a multiple of the other, like x + 2y = 5 and 2x + 4y = 10, every point on the line works. The answer is then written as x = 5 − 2y, with y free to be any real number.

How do you type a problem into the algebra calculator?

Type it the way you'd write it on one line of a keyboard. Use ^ for powers, / for fractions, and any single letter for the variable.

Spaces don't matter, and 2x means 2 times x, so you don't need a multiplication sign. When a fraction has more than one term on top, wrap it in parentheses: (x + 1)/3, not x + 1/3. The same goes for a negative number you're substituting, so write 2(−3), not 2−3.

You can also paste text straight from a worksheet. Instructions like "Solve for b:" or "Factor completely:" are read and used, so "Solve for b: 2b − 5 = 9" gives b = 7. For systems, separate the equations with commas or semicolons and choose Solve system from the menu, since Solve expects a single equation.

How does the answer check work?

After solving an equation, the solver puts the answer back into the original problem and confirms both sides come out equal. For 2(x + 3) = 14 it plugs in 4 and gets 14 = 14.

With two answers, as in a quadratic, each one is checked on its own. For |2x − 3| = 7 it tests x = 5 and x = −2 separately, and both give 7. For factoring, expanding and simplifying, it confirms the new form is equivalent to what you typed, so (x + 3)(x − 3) multiplies back to x² − 9.

Answers stay exact wherever possible. You'll see −2 + √3, not −0.2679. A decimal approximation only appears when a polynomial has no exact form the solver can reach.

Inequalities get a different kind of check. For a quadratic inequality such as x² − 5x + 6 ≥ 0, the solver tests one number in each interval of a sign chart and keeps the intervals that pass. You can see each test value and its result, so it's easy to confirm by hand.

How can you use an algebra solver to learn instead of copy?

Do the problem yourself first, then use the solver to check. Copying steps you haven't tried tends to fall apart on a test, because the test asks you to start from a blank line.

A routine that works well for homework:

1. Work the problem on paper and circle your answer.
2. Type the problem in and compare only the final answer.
3. If they match, move on. If not, read the steps from the top and find the first line where your work differs.
4. Fix that line on your own paper and finish without looking again.
5. Try a similar problem with new numbers to see if the fix sticks.

Step 3 is where the learning happens. Most wrong answers come from one slip, like a dropped negative or a 6 that should have been subtracted from both sides. Finding your own slip teaches more than reading a full solution.

Parents and tutors can use the same idea in reverse. Cover the steps, ask the student to say what the next line should be, then reveal it. Predicting a step is harder than reading one, and that effort is what makes the method stick.

It also helps to rerun the solver with your own wrong answer in mind. If you got x = 5.5 for 2(x + 3) = 14, put 5.5 into the original equation yourself. Seeing 2(8.5) = 17 instead of 14 shows you the answer is off before you go looking for why.

What mistakes does the solver catch most often?

The most common one is distributing to only the first term. In 2(x + 3) the 2 multiplies both the x and the 3, giving 2x + 6. Writing 2x + 3 leads to x = 5.5, which fails the check.

Sign errors come next. Subtracting a negative, or forgetting to flip an inequality when you divide by a negative, changes the answer completely. In −3x + 6 > 15 the correct result is x < −3, and the solver marks the flip as its own step so you can see it.

A third one is stopping at one root. x² = 9 has two answers, x = −3 and x = 3, and losing the negative one is easy when you take a square root in your head.