Determine the real solutions of inequality (x-4)(x+8)

First, we'll remove the brackets both sides. We'll apply
FOIL method to multiply the terms inside brackets:

x^2 + 8x
- 4x - 32 < x^2 + 4x - 8x - 32

We'll move all terms
to the left side:

x^2 + 8x - 4x - 32 - x^2 - 4x + 8x + 32
< 0

We'll combine like terms and we'll eliminate
like terms:

8x <
0

We'll divide by 8:

x
< 0

The solution for the inequality
is: x < 0 <=>(-infinite ;
0).