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

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

X(X+3)=-2(X+3)

We move all terms to the left:

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

We multiply parentheses

X^2+3X-(-2(X+3))=0


We calculate terms in parentheses: -(-2(X+3)), so:

-2(X+3)

We multiply parentheses

-2X-6

Back to the equation:

-(-2X-6)


We get rid of parentheses

X^2+3X+2X+6=0

We add all the numbers together, and all the variables

X^2+5X+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:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-1}{2*1}=\frac{-6}{2}
=-3
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+1}{2*1}=\frac{-4}{2}
=-2
$