3(2n+3)(n-4)=0

Solution for 3(2n+3)(n-4)=0 equation:

3(2n+3)(n-4)=0

We multiply parentheses ..

3(+2n^2-8n+3n-12)=0

We multiply parentheses

6n^2-24n+9n-36=0

We add all the numbers together, and all the variables

6n^2-15n-36=0

a = 6; b = -15; c = -36;
Δ = b2-4ac
Δ = -152-4·6·(-36)
Δ = 1089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1089}=33$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-33}{2*6}=\frac{-18}{12}
=-1+1/2
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+33}{2*6}=\frac{48}{12}
=4
$