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

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

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

We move all terms to the left:

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

We multiply parentheses

6x^2+9x-(-2x-3)=0

We get rid of parentheses

6x^2+9x+2x+3=0

We add all the numbers together, and all the variables

6x^2+11x+3=0

a = 6; b = 11; c = +3;
Δ = b2-4ac
Δ = 112-4·6·3
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-7}{2*6}=\frac{-18}{12}
=-1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+7}{2*6}=\frac{-4}{12}
=-1/3
$