(9+3n)(5-7n)=0

Solution for (9+3n)(5-7n)=0 equation:

(9+3n)(5-7n)=0

We add all the numbers together, and all the variables

(3n+9)(-7n+5)=0

We multiply parentheses ..

(-21n^2+15n-63n+45)=0

We get rid of parentheses

-21n^2+15n-63n+45=0

We add all the numbers together, and all the variables

-21n^2-48n+45=0

a = -21; b = -48; c = +45;
Δ = b2-4ac
Δ = -482-4·(-21)·45
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{-(-48)-78}{2*-21}=\frac{-30}{-42}
=5/7
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+78}{2*-21}=\frac{126}{-42}
=-3
$