Y=(-x-2)(x+3)

Solution for Y=(-x-2)(x+3) equation:

=(-Y-2)(Y+3)

We move all terms to the left:

-((-Y-2)(Y+3))=0

We add all the numbers together, and all the variables

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

We multiply parentheses ..

-((-1Y^2-3Y-2Y-6))=0


We calculate terms in parentheses: -((-1Y^2-3Y-2Y-6)), so:

(-1Y^2-3Y-2Y-6)

We get rid of parentheses

-1Y^2-3Y-2Y-6

We add all the numbers together, and all the variables

-1Y^2-5Y-6

Back to the equation:

-(-1Y^2-5Y-6)


We get rid of parentheses

1Y^2+5Y+6=0

We add all the numbers together, and all the variables

Y^2+5Y+6=0

a = 1; b = 5; c = +6;
Δ = b2-4ac
Δ = 52-4·1·6
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{-(5)-1}{2*1}=\frac{-6}{2}
=-3
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+1}{2*1}=\frac{-4}{2}
=-2
$