-3n(5n+3)=0

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

-3n(5n+3)=0

We multiply parentheses

-15n^2-9n=0

a = -15; b = -9; c = 0;
Δ = b2-4ac
Δ = -92-4·(-15)·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-9}{2*-15}=\frac{0}{-30}
=0
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+9}{2*-15}=\frac{18}{-30}
=-3/5
$