(y+3)(y+2)=2y+5y+6

Solution for (y+3)(y+2)=2y+5y+6 equation:

(y+3)(y+2)=2y+5y+6

We move all terms to the left:

(y+3)(y+2)-(2y+5y+6)=0

We add all the numbers together, and all the variables

(y+3)(y+2)-(7y+6)=0

We get rid of parentheses

(y+3)(y+2)-7y-6=0

We multiply parentheses ..

(+y^2+2y+3y+6)-7y-6=0

We get rid of parentheses

y^2+2y+3y-7y+6-6=0

We add all the numbers together, and all the variables

y^2-2y=0

a = 1; b = -2; c = 0;
Δ = b2-4ac
Δ = -22-4·1·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2}{2*1}=\frac{0}{2}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2}{2*1}=\frac{4}{2}
=2
$