12(n+11)(3n-4)=0

Solution for 12(n+11)(3n-4)=0 equation:

12(n+11)(3n-4)=0

We multiply parentheses ..

12(+3n^2-4n+33n-44)=0

We multiply parentheses

36n^2-48n+396n-528=0

We add all the numbers together, and all the variables

36n^2+348n-528=0

a = 36; b = 348; c = -528;
Δ = b2-4ac
Δ = 3482-4·36·(-528)
Δ = 197136
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{197136}=444$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(348)-444}{2*36}=\frac{-792}{72}
=-11
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(348)+444}{2*36}=\frac{96}{72}
=1+1/3
$