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

Solution for 6(n-2)(5n+3)=0 equation:

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

We multiply parentheses ..

6(+5n^2+3n-10n-6)=0

We multiply parentheses

30n^2+18n-60n-36=0

We add all the numbers together, and all the variables

30n^2-42n-36=0

a = 30; b = -42; c = -36;
Δ = b2-4ac
Δ = -422-4·30·(-36)
Δ = 6084
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6084}=78$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-78}{2*30}=\frac{-36}{60}
=-3/5
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+78}{2*30}=\frac{120}{60}
=2
$