(3n-9)(2n+12)=0

Solution for (3n-9)(2n+12)=0 equation:

(3n-9)(2n+12)=0

We multiply parentheses ..

(+6n^2+36n-18n-108)=0

We get rid of parentheses

6n^2+36n-18n-108=0

We add all the numbers together, and all the variables

6n^2+18n-108=0

a = 6; b = 18; c = -108;
Δ = b2-4ac
Δ = 182-4·6·(-108)
Δ = 2916
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2916}=54$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-54}{2*6}=\frac{-72}{12}
=-6
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+54}{2*6}=\frac{36}{12}
=3
$