(3y+7)(2y+3)=0

Solution for (3y+7)(2y+3)=0 equation:

(3y+7)(2y+3)=0

We multiply parentheses ..

(+6y^2+9y+14y+21)=0

We get rid of parentheses

6y^2+9y+14y+21=0

We add all the numbers together, and all the variables

6y^2+23y+21=0

a = 6; b = 23; c = +21;
Δ = b2-4ac
Δ = 232-4·6·21
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(23)-5}{2*6}=\frac{-28}{12}
=-2+1/3
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+5}{2*6}=\frac{-18}{12}
=-1+1/2
$