(n-6)(n+1)=n-6

Solution for (n-6)(n+1)=n-6 equation:

(n-6)(n+1)=n-6

We move all terms to the left:

(n-6)(n+1)-(n-6)=0

We get rid of parentheses

(n-6)(n+1)-n+6=0

We multiply parentheses ..

(+n^2+n-6n-6)-n+6=0

We add all the numbers together, and all the variables

(+n^2+n-6n-6)-1n+6=0

We get rid of parentheses

n^2+n-6n-1n-6+6=0

We add all the numbers together, and all the variables

n^2-6n=0

a = 1; b = -6; c = 0;
Δ = b2-4ac
Δ = -62-4·1·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6}{2*1}=\frac{0}{2}
=0
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6}{2*1}=\frac{12}{2}
=6
$