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

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

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

We multiply parentheses ..

(+2y^2+7y+6y+21)=0

We get rid of parentheses

2y^2+7y+6y+21=0

We add all the numbers together, and all the variables

2y^2+13y+21=0

a = 2; b = 13; c = +21;
Δ = b2-4ac
Δ = 132-4·2·21
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-1}{2*2}=\frac{-14}{4}
=-3+1/2
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+1}{2*2}=\frac{-12}{4}
=-3
$