3(5n+1)(n-2)=0

Solution for 3(5n+1)(n-2)=0 equation:

3(5n+1)(n-2)=0

We multiply parentheses ..

3(+5n^2-10n+n-2)=0

We multiply parentheses

15n^2-30n+3n-6=0

We add all the numbers together, and all the variables

15n^2-27n-6=0

a = 15; b = -27; c = -6;
Δ = b2-4ac
Δ = -272-4·15·(-6)
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{-(-27)-33}{2*15}=\frac{-6}{30}
=-1/5
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+33}{2*15}=\frac{60}{30}
=2
$