How to Factor Equations

By Ainsley Patterson; Updated April 24, 2017
A quadratic equation's factors are expressions with two terms.

One way of solving quadratic equations is by factoring the equation and then solving each part of the equation for zero.

Factoring Quadratic Equations

Solve the equation for zero.

Example: (x^2)-7x=18 --->(x^2)-7x-18=0 by subtracting 18 from both sides.

Factor the left side of the equation by determining two numbers that add up to, in this case, -7, and can be multiplied together to get -18.

Example: -9 and 2 -9*2=-18 -9+2=-7

Put the left side of the quadratic equation into two factors that can multiplied out to get the original quadratic equation.

Example: (x-9)(x+2)=0

Because x_x=x^2 -9x+2x=-7x -9_2=-18

So you can see that all the elements of the original quadratic equation are there.

Solve each factor of the equation for zero to get your solution set for the quadratic equation.

Example: x-9=0 so x=9 x+2=0 so x=-2

So, your solution set for the equation is {9, -2}

About the Author

Based in Ypsilanti, Mich., Ainsley Patterson has been a freelance writer since 2007. Her articles appear on various websites. She especially enjoys utilizing her more than 10 years of craft and sewing experience to write tutorials. Patterson is working on her bachelor's degree in liberal arts at the University of Michigan.