-2y(-2y+2)-2(3y+6)=6

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

-2y(-2y+2)-2(3y+6)=6

We move all terms to the left:

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

We multiply parentheses

4y^2-4y-6y-12-6=0

We add all the numbers together, and all the variables

4y^2-10y-18=0

a = 4; b = -10; c = -18;
Δ = b2-4ac
Δ = -102-4·4·(-18)
Δ = 388
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:

$\sqrt{\Delta}=\sqrt{388}=\sqrt{4*97}=\sqrt{4}*\sqrt{97}=2\sqrt{97}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{97}}{2*4}=\frac{10-2\sqrt{97}}{8}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{97}}{2*4}=\frac{10+2\sqrt{97}}{8}
$