(2n)(-3n-2)=3n-3

Solution for (2n)(-3n-2)=3n-3 equation:

(2n)(-3n-2)=3n-3

We move all terms to the left:

(2n)(-3n-2)-(3n-3)=0

We multiply parentheses

-6n^2-4n-(3n-3)=0

We get rid of parentheses

-6n^2-4n-3n+3=0

We add all the numbers together, and all the variables

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

a = -6; b = -7; c = +3;
Δ = b2-4ac
Δ = -72-4·(-6)·3
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-11}{2*-6}=\frac{-4}{-12}
=1/3
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+11}{2*-6}=\frac{18}{-12}
=-1+1/2
$