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

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

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

We multiply parentheses ..

-3(+2x^2-3x+4x-6)=0

We multiply parentheses

-6x^2+9x-12x+18=0

We add all the numbers together, and all the variables

-6x^2-3x+18=0

a = -6; b = -3; c = +18;
Δ = b2-4ac
Δ = -32-4·(-6)·18
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-21}{2*-6}=\frac{-18}{-12}
=1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+21}{2*-6}=\frac{24}{-12}
=-2
$