Solve for x:  x^{2} + 5x + 6 = 0 
List pairs of numbers that multiply together to get 6:  1 * 6 = 6, 2 * 3 = 6, 1 * 6 = 6, 2 * 3 = 6 
From the pairs above, find the pair that adds up to 5:  2 + 3 = 5 
These two numbers (2 & 3) are used to determine the factors.  (x + 2) (x + 3) = 0. 
Set each factor equal to 0:  x + 2 = 0 , x + 3 = 0 
Solve each equation:  x = 2, x = 3 
Another example:  x^{2} + 2x  15 = 0 
List pairs of numbers that multiply together to get 15:  1 * 15 = 15, 1 * 15 = 15, 3 * 5 = 15, 3 * 5 = 15 
From the pairs above, find the pair that adds up to 2:  3 + 5 = 2 
These two numbers (3 & 5) are used in the factors.  (x  3) (x + 5) = 0. 
Set each factor equal to 0:  x  3 = 0 , x + 5 = 0 
Solve each equation:  x = 3, x = 5 


