(2y-12)(3y+15)=0

Solution for (2y-12)(3y+15)=0 equation:

(2y-12)(3y+15)=0

We multiply parentheses ..

(+6y^2+30y-36y-180)=0

We get rid of parentheses

6y^2+30y-36y-180=0

We add all the numbers together, and all the variables

6y^2-6y-180=0

a = 6; b = -6; c = -180;
Δ = b2-4ac
Δ = -62-4·6·(-180)
Δ = 4356
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4356}=66$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-66}{2*6}=\frac{-60}{12}
=-5
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+66}{2*6}=\frac{72}{12}
=6
$