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

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

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

We multiply parentheses ..

(+15n^2+9n+5n+3)=0

We get rid of parentheses

15n^2+9n+5n+3=0

We add all the numbers together, and all the variables

15n^2+14n+3=0

a = 15; b = 14; c = +3;
Δ = b2-4ac
Δ = 142-4·15·3
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-4}{2*15}=\frac{-18}{30}
=-3/5
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+4}{2*15}=\frac{-10}{30}
=-1/3
$