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

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We have to find all the real solution of (x-4)(x+8) < (x-8)(x+4).

(x-4)(x+8) < (x-8)(x+4)

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

=> -4x + 8x < -8x + 4x

=> 4x < -4x

=> 8x < 0

=> x < 0

**The values are all real numbers x satisfying the relation x < 0**

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).**