(n-6)(3n+21)=0

Solution for (n-6)(3n+21)=0 equation:

(n-6)(3n+21)=0

We multiply parentheses ..

(+3n^2+21n-18n-126)=0

We get rid of parentheses

3n^2+21n-18n-126=0

We add all the numbers together, and all the variables

3n^2+3n-126=0

a = 3; b = 3; c = -126;
Δ = b2-4ac
Δ = 32-4·3·(-126)
Δ = 1521
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1521}=39$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-39}{2*3}=\frac{-42}{6}
=-7
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+39}{2*3}=\frac{36}{6}
=6
$