Example 10:  Solve (2x – 3)(x + 5) = 7

Solution:  We cannot conclude that one of the factors on the left is 7, since 7 does not share the 0 product property.  So we must expand the left side, subtract 7, and then factor the left side:

(2x – 3)(x + 5) = 7

2x² + 7x – 15 = 7

2x² + 7x – 22 = 0

(2x + 11)(x – 2) = 0

Now set each factor equal to 0 and solve:

2x + 11 = 0   -->   2x = –11  -->   x = –5.5

x – 2 = 0   -->   x = 2

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