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

Solution for 12(x-4)(3x+2)=0 equation:

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

We multiply parentheses ..

12(+3x^2+2x-12x-8)=0

We multiply parentheses

36x^2+24x-144x-96=0

We add all the numbers together, and all the variables

36x^2-120x-96=0

a = 36; b = -120; c = -96;
Δ = b2-4ac
Δ = -1202-4·36·(-96)
Δ = 28224
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{28224}=168$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-120)-168}{2*36}=\frac{-48}{72}
=-2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-120)+168}{2*36}=\frac{288}{72}
=4
$