How To Factor Equations

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

Step 1

Solve the equation for zero.

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

Step 2

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

Step 3

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 xx=x^2 -9x+2x=-7x -92=-18

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

Step 4

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}