-4*(2y+6)*y=0

Solution for -4*(2y+6)*y=0 equation:

-4(2y+6)*y=0

We multiply parentheses

-8y^2-24y=0

a = -8; b = -24; c = 0;
Δ = b2-4ac
Δ = -242-4·(-8)·0
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-24}{2*-8}=\frac{0}{-16}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+24}{2*-8}=\frac{48}{-16}
=-3
$