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

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

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

We multiply parentheses ..

2(+3x^2-2x+18x-12)=0

We multiply parentheses

6x^2-4x+36x-24=0

We add all the numbers together, and all the variables

6x^2+32x-24=0

a = 6; b = 32; c = -24;
Δ = b2-4ac
Δ = 322-4·6·(-24)
Δ = 1600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1600}=40$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-40}{2*6}=\frac{-72}{12}
=-6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+40}{2*6}=\frac{8}{12}
=2/3
$