(3x-12)(4x+16)=0

Solution for (3x-12)(4x+16)=0 equation:

(3x-12)(4x+16)=0

We multiply parentheses ..

(+12x^2+48x-48x-192)=0

We get rid of parentheses

12x^2+48x-48x-192=0

We add all the numbers together, and all the variables

12x^2-192=0

a = 12; b = 0; c = -192;
Δ = b2-4ac
Δ = 02-4·12·(-192)
Δ = 9216
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9216}=96$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-96}{2*12}=\frac{-96}{24}
=-4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+96}{2*12}=\frac{96}{24}
=4
$