3(2y+1)(3y-1)=0

Solution for 3(2y+1)(3y-1)=0 equation:

3(2y+1)(3y-1)=0

We multiply parentheses ..

3(+6y^2-2y+3y-1)=0

We multiply parentheses

18y^2-6y+9y-3=0

We add all the numbers together, and all the variables

18y^2+3y-3=0

a = 18; b = 3; c = -3;
Δ = b2-4ac
Δ = 32-4·18·(-3)
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-15}{2*18}=\frac{-18}{36}
=-1/2
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+15}{2*18}=\frac{12}{36}
=1/3
$