How do you use factoring in quadratic equations?

To solve a quadratic equation by factoring, follow this five-step process:

  1. Put all terms on one side of the equal sign, leaving zero on the other side.
  2. Factor.
  3. Set each factor equal to zero.
  4. Solve each of these equations.
  5. Check by inserting your answer in the original equation.

Example: Solve x2 – 6x = 16.

Following the steps,

x2 - 6x becomes x2 - 6x - 16 = 0 

Factor

(x - 8)(x + 2) = 0 
x - 8 = 0 or x + 2 = 0 
x = 8 x = -2 

Then to check,

82 - 6(8) = 16 or (-2)2 - 6(-2) = 16 
64 - 48 = 16 4 + 12 = 16 
16 = 16 16 = 16 

Both values, 8 and –2, are solutions to the original equation.