(3n+6)*(6n-3)=0

Solution for (3n+6)*(6n-3)=0 equation:

(3n+6)(6n-3)=0

We multiply parentheses ..

(+18n^2-9n+36n-18)=0

We get rid of parentheses

18n^2-9n+36n-18=0

We add all the numbers together, and all the variables

18n^2+27n-18=0

a = 18; b = 27; c = -18;
Δ = b2-4ac
Δ = 272-4·18·(-18)
Δ = 2025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2025}=45$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-45}{2*18}=\frac{-72}{36}
=-2
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+45}{2*18}=\frac{18}{36}
=1/2
$