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

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

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

We multiply parentheses ..

(+9y^2-27y+18y-54)=0

We get rid of parentheses

9y^2-27y+18y-54=0

We add all the numbers together, and all the variables

9y^2-9y-54=0

a = 9; b = -9; c = -54;
Δ = b2-4ac
Δ = -92-4·9·(-54)
Δ = 2025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2025}=45$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-45}{2*9}=\frac{-36}{18}
=-2
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+45}{2*9}=\frac{54}{18}
=3
$