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

Solution for 6(2x+3)(x-2)=0 equation:

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

We multiply parentheses ..

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

We multiply parentheses

12x^2-24x+18x-36=0

We add all the numbers together, and all the variables

12x^2-6x-36=0

a = 12; b = -6; c = -36;
Δ = b2-4ac
Δ = -62-4·12·(-36)
Δ = 1764
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1764}=42$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-42}{2*12}=\frac{-36}{24}
=-1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+42}{2*12}=\frac{48}{24}
=2
$