How Do You Solve by Factoring?


Quick Answer

To solve by factoring, move all terms to the same side of the equation with subtraction or addition, and then find each factor in the equation. Setting each factor at zero provides all of the solutions to the equation.

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Full Answer

  1. Move all terms to one side of the equation

    Consider the problem x^2 + 3x = -25 - 7x. Subtract both (-25) and (-7x) from both sides to yield the next step: x^2 + 10x + 25 = 0. Remember that subtracting a negative number is equivalent to adding a positive number with the same value.

  2. Factor the trinomial to find the solutions

    Look at the constant term in the equation, and identify its factors. Consider the example question: x^2 + 10x + 25 = 0; the constant term is 25, with factors 1 and 5. Choose the pair of factors that multiplies together to make 25 while also adding up to the constant multiplied by the "x" term (10). Write the pair of factors this way: (x+5)(x+5) = 0. Write the solution as x = -5.

  3. Test the solution

    Plug each of the solutions into the original equation to see if the equation holds up. Use the example question to test: (-5)^2 + 3(-5) = -25 - 7(-5). Multiply out to yield 25 - 15 = -25 -(-35), or 10 = 10.

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