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
$