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
$