-4(x+3)(2x-8)=0

Solution for -4(x+3)(2x-8)=0 equation:

-4(x+3)(2x-8)=0

We multiply parentheses ..

-4(+2x^2-8x+6x-24)=0

We multiply parentheses

-8x^2+32x-24x+96=0

We add all the numbers together, and all the variables

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

a = -8; b = 8; c = +96;
Δ = b2-4ac
Δ = 82-4·(-8)·96
Δ = 3136
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3136}=56$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-56}{2*-8}=\frac{-64}{-16}
=+4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+56}{2*-8}=\frac{48}{-16}
=-3
$