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

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

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

We multiply parentheses ..

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

We multiply parentheses

-6x^2-9x+24x+36=0

We add all the numbers together, and all the variables

-6x^2+15x+36=0

a = -6; b = 15; c = +36;
Δ = b2-4ac
Δ = 152-4·(-6)·36
Δ = 1089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1089}=33$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-33}{2*-6}=\frac{-48}{-12}
=+4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+33}{2*-6}=\frac{18}{-12}
=-1+1/2
$