Algebra calculator, simplify and solve with steps.

An algebra calculator simplifies expressions and solves equations, and shows how it got there. Type 2x + 3 = 11 and it solves for x. Type (x^2 − 4)/(x − 2) and it simplifies to x + 2. It also expands brackets, factors polynomials, solves quadratics with exact square roots or complex answers, finds the rational roots of cubics and higher, and clears fractions that have x in the bottom.

How to use the algebra calculator

1. Type an expression or an equation in the box. Use ^ for powers, / for division, and brackets where needed. Multiplication can be left out.
2. Leave Do on Auto. An equals sign means solve, and no equals sign means simplify. Or choose Simplify, Expand, Factor or Solve.
3. If the equation has more than one letter, pick the one to solve for under Solve for. Auto uses x when it is there.
4. Read the answer cards, then open the steps. For equations a graph shows the left and right side, with dots where they meet.

Solving a linear equation

Take 2x + 3 = 11. Subtract 3 from both sides to get 2x = 8, then divide by 2 to get x = 4. Check: 2 times 4 plus 3 is 11. For 3(x − 2) = 2(x + 1), multiply out to 3x − 6 = 2x + 2, which becomes x − 8 = 0 after moving everything to one side, so x = 8. Check: 3 times 6 is 18 and 2 times 9 is 18.

Solving a quadratic equation

A quadratic is a x^2 + b x + c = 0. The discriminant b^2 − 4ac tells you what to expect. Above 0 gives two real roots, 0 gives one repeated root, and below 0 gives two complex roots. The formula is x = (−b ± the square root of the discriminant) / 2a.

Higher degree equations

For a cubic or higher, the calculator first looks for rational roots. Any rational root p/q has p dividing the constant term and q dividing the leading coefficient. For x^3 − 6x^2 + 11x − 6 = 0 the constant is −6, so it tries 1, 2, 3, 6 and their negatives, and finds 1, 2 and 3. Then the equation factors as (x − 1)(x − 2)(x − 3). If some roots are not rational, they are found as decimals and marked as decimals, because there is no neat exact form to show.

Fractions with x in the bottom

Take (x^2 − 1)/(x − 1) = 2. Clearing the fraction and moving terms gives x^2 − 2x + 1 = 0, whose only root is x = 1. But x = 1 makes the bottom 0, so the original equation is not defined there, and the answer is no solution. The calculator throws out such values and tells you why. For 1/x + 1/(x + 1) = 1 the roots are (1 ± √5)/2, and neither makes a bottom zero.

Simplifying, expanding and factoring

(x^2 − 4)/(x − 2) factors on top as (x − 2)(x + 2), the (x − 2) cancels, and the result is x + 2 for every x except 2. (x + 1)^2 − (x − 1)^2 expands to x^2 + 2x + 1 − x^2 + 2x − 1, which is 4x. Factoring needs one letter and whole-number factors: x^4 − 5x^2 + 4 becomes (x − 1)(x + 1)(x − 2)(x + 2).

Letters as constants

With several letters, degree 1 and 2 equations still work. a x + b = c solved for x gives x = (c − b)/a. Solving a x^2 + b x + c = 0 for x gives the quadratic formula with a, b and c in it.

What it cannot do

It does not solve inequalities, absolute value equations, equations with the unknown inside a root, log or trig function, or equations like 2^x = 8. It does not factor with letters other than one variable. When it meets one of these, it says so instead of guessing.

For a system with two or more equations, use the . For the factors of a plain number, try the factor calculator, and to see an equation as a curve use the graphing calculator.