-6y(-3y-15)+6y=-6

Solution for -6y(-3y-15)+6y=-6 equation:

-6y(-3y-15)+6y=-6

We move all terms to the left:

-6y(-3y-15)+6y-(-6)=0

We add all the numbers together, and all the variables

6y-6y(-3y-15)+6=0

We multiply parentheses

18y^2+6y+90y+6=0

We add all the numbers together, and all the variables

18y^2+96y+6=0

a = 18; b = 96; c = +6;
Δ = b2-4ac
Δ = 962-4·18·6
Δ = 8784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{8784}=\sqrt{144*61}=\sqrt{144}*\sqrt{61}=12\sqrt{61}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(96)-12\sqrt{61}}{2*18}=\frac{-96-12\sqrt{61}}{36}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(96)+12\sqrt{61}}{2*18}=\frac{-96+12\sqrt{61}}{36}
$