(9n+12)(15n-6)=180

Solution for (9n+12)(15n-6)=180 equation:

(9n+12)(15n-6)=180

We move all terms to the left:

(9n+12)(15n-6)-(180)=0

We multiply parentheses ..

(+135n^2-54n+180n-72)-180=0

We get rid of parentheses

135n^2-54n+180n-72-180=0

We add all the numbers together, and all the variables

135n^2+126n-252=0

a = 135; b = 126; c = -252;
Δ = b2-4ac
Δ = 1262-4·135·(-252)
Δ = 151956
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{151956}=\sqrt{324*469}=\sqrt{324}*\sqrt{469}=18\sqrt{469}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(126)-18\sqrt{469}}{2*135}=\frac{-126-18\sqrt{469}}{270}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(126)+18\sqrt{469}}{2*135}=\frac{-126+18\sqrt{469}}{270}
$