Find two common factors that not only multiply to give the constant "c" but also add up to equal "b," which is the coefficient on the "x" variable. For example, if the quadratic equation was "x^2 + 5x + 6" then the constant "c" would be 6 and the coefficient "b" would be 5. The two numbers to be ascertained for this example would need to add together to equal 5 and also multiply together to equal 6; this would therefore be 2 and 3.
Write the two common factors in the form: "(x + m)(x + n) = 0." The two factors would therefore take the place of the "m" and "n" variables. For example, for the quadratic equation "x^2 + 5x + 6 = 0" would equal "(x + 2)(x + 3)."
Solve both of the factors by making each of them equal to zero one at a time. For example, if the factored quadratic equation is "(x + 2)(x + 3) = 0" then solving "(x + 2) = 0" would make "x" equal to -2 and solving "(x + 3) = 0" would make "x" equal to -3.
Check the values of "x" are correct for your quadratic equation by placing the values into the expression. For example, if the factored quadratic equation is "x^2 + 5x + 6 = 0," then substituting "x" for the value -2 would make the expression equal to "(-2)^2 + 5(-2) + 6 = 0," which is true when the left side of the expression if simplified.