(5n+3)(6n-7)=0

Solution for (5n+3)(6n-7)=0 equation:

(5n+3)(6n-7)=0

We multiply parentheses ..

(+30n^2-35n+18n-21)=0

We get rid of parentheses

30n^2-35n+18n-21=0

We add all the numbers together, and all the variables

30n^2-17n-21=0

a = 30; b = -17; c = -21;
Δ = b2-4ac
Δ = -172-4·30·(-21)
Δ = 2809
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2809}=53$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-53}{2*30}=\frac{-36}{60}
=-3/5
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+53}{2*30}=\frac{70}{60}
=1+1/6
$