3(x-12)(x+15)=0

Solution for 3(x-12)(x+15)=0 equation:

3(x-12)(x+15)=0

We multiply parentheses ..

3(+x^2+15x-12x-180)=0

We multiply parentheses

3x^2+45x-36x-540=0

We add all the numbers together, and all the variables

3x^2+9x-540=0

a = 3; b = 9; c = -540;
Δ = b2-4ac
Δ = 92-4·3·(-540)
Δ = 6561
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6561}=81$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-81}{2*3}=\frac{-90}{6}
=-15
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+81}{2*3}=\frac{72}{6}
=12
$