(4x-16)(x+12)=0

Solution for (4x-16)(x+12)=0 equation:

(4x-16)(x+12)=0

We multiply parentheses ..

(+4x^2+48x-16x-192)=0

We get rid of parentheses

4x^2+48x-16x-192=0

We add all the numbers together, and all the variables

4x^2+32x-192=0

a = 4; b = 32; c = -192;
Δ = b2-4ac
Δ = 322-4·4·(-192)
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*4}=\frac{-96}{8}
=-12
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+64}{2*4}=\frac{32}{8}
=4
$