-3y(3y+4)=-12

Solution for -3y(3y+4)=-12 equation:

-3y(3y+4)=-12

We move all terms to the left:

-3y(3y+4)-(-12)=0

We add all the numbers together, and all the variables

-3y(3y+4)+12=0

We multiply parentheses

-9y^2-12y+12=0

a = -9; b = -12; c = +12;
Δ = b2-4ac
Δ = -122-4·(-9)·12
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{-(-12)-24}{2*-9}=\frac{-12}{-18}
=2/3
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+24}{2*-9}=\frac{36}{-18}
=-2
$