(4x+8)(8x-16)=0

Solution for (4x+8)(8x-16)=0 equation:

(4x+8)(8x-16)=0

We multiply parentheses ..

(+32x^2-64x+64x-128)=0

We get rid of parentheses

32x^2-64x+64x-128=0

We add all the numbers together, and all the variables

32x^2-128=0

a = 32; b = 0; c = -128;
Δ = b2-4ac
Δ = 02-4·32·(-128)
Δ = 16384
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16384}=128$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-128}{2*32}=\frac{-128}{64}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+128}{2*32}=\frac{128}{64}
=2
$