(3n-7)(2n-6)=0

Solution for (3n-7)(2n-6)=0 equation:

(3n-7)(2n-6)=0

We multiply parentheses ..

(+6n^2-18n-14n+42)=0

We get rid of parentheses

6n^2-18n-14n+42=0

We add all the numbers together, and all the variables

6n^2-32n+42=0

a = 6; b = -32; c = +42;
Δ = b2-4ac
Δ = -322-4·6·42
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{-(-32)-4}{2*6}=\frac{28}{12}
=2+1/3
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+4}{2*6}=\frac{36}{12}
=3
$