(2x-12)(4x+8)=0

Solution for (2x-12)(4x+8)=0 equation:

(2x-12)(4x+8)=0

We multiply parentheses ..

(+8x^2+16x-48x-96)=0

We get rid of parentheses

8x^2+16x-48x-96=0

We add all the numbers together, and all the variables

8x^2-32x-96=0

a = 8; b = -32; c = -96;
Δ = b2-4ac
Δ = -322-4·8·(-96)
Δ = 4096
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4096}=64$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-64}{2*8}=\frac{-32}{16}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+64}{2*8}=\frac{96}{16}
=6
$