3(x-5)(6x+12)=0

Solution for 3(x-5)(6x+12)=0 equation:

3(x-5)(6x+12)=0

We multiply parentheses ..

3(+6x^2+12x-30x-60)=0

We multiply parentheses

18x^2+36x-90x-180=0

We add all the numbers together, and all the variables

18x^2-54x-180=0

a = 18; b = -54; c = -180;
Δ = b2-4ac
Δ = -542-4·18·(-180)
Δ = 15876
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{15876}=126$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-54)-126}{2*18}=\frac{-72}{36}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-54)+126}{2*18}=\frac{180}{36}
=5
$