(6n-3)(3n+12)=0

Solution for (6n-3)(3n+12)=0 equation:

(6n-3)(3n+12)=0

We multiply parentheses ..

(+18n^2+72n-9n-36)=0

We get rid of parentheses

18n^2+72n-9n-36=0

We add all the numbers together, and all the variables

18n^2+63n-36=0

a = 18; b = 63; c = -36;
Δ = b2-4ac
Δ = 632-4·18·(-36)
Δ = 6561
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6561}=81$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(63)-81}{2*18}=\frac{-144}{36}
=-4
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(63)+81}{2*18}=\frac{18}{36}
=1/2
$