(9y+3)(-2y-6)=0

Solution for (9y+3)(-2y-6)=0 equation:

(9y+3)(-2y-6)=0

We multiply parentheses ..

(-18y^2-54y-6y-18)=0

We get rid of parentheses

-18y^2-54y-6y-18=0

We add all the numbers together, and all the variables

-18y^2-60y-18=0

a = -18; b = -60; c = -18;
Δ = b2-4ac
Δ = -602-4·(-18)·(-18)
Δ = 2304
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2304}=48$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-48}{2*-18}=\frac{12}{-36}
=-1/3
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+48}{2*-18}=\frac{108}{-36}
=-3
$