The quadratic in equality (x + 2)(x + 5) > 0.

Now, there are two ways that this product could be greater than zero (positive) -- both factors are positive or both factors are negative. You must check out both possibilities.

Both positive:

(x + 2) > 0 and (x + 5) > 0

x > - 2 and x > - 5

The only condition that makes both true is x > - 2.

Both negative:

(x + 2) < 0 and (x + 5) < 0

x < - 2 and x < - 5

The only condition that makes both true is x < - 5.

Final answer:  x < - 5  or  x > - 2.

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