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

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

Simplifying
(n + -6)(n + 6) = n + -6

Reorder the terms:
(-6 + n)(n + 6) = n + -6

Reorder the terms:
(-6 + n)(6 + n) = n + -6

Multiply (-6 + n) * (6 + n)
(-6(6 + n) + n(6 + n)) = n + -6
((6 * -6 + n * -6) + n(6 + n)) = n + -6
((-36 + -6n) + n(6 + n)) = n + -6
(-36 + -6n + (6 * n + n * n)) = n + -6
(-36 + -6n + (6n + n2)) = n + -6

Combine like terms: -6n + 6n = 0
(-36 + 0 + n2) = n + -6
(-36 + n2) = n + -6

Reorder the terms:
-36 + n2 = -6 + n

Solving
-36 + n2 = -6 + n

Solving for variable 'n'.

Reorder the terms:
-36 + 6 + -1n + n2 = -6 + n + 6 + -1n

Combine like terms: -36 + 6 = -30
-30 + -1n + n2 = -6 + n + 6 + -1n

Reorder the terms:
-30 + -1n + n2 = -6 + 6 + n + -1n

Combine like terms: -6 + 6 = 0
-30 + -1n + n2 = 0 + n + -1n
-30 + -1n + n2 = n + -1n

Combine like terms: n + -1n = 0
-30 + -1n + n2 = 0

Factor a trinomial.
(-5 + -1n)(6 + -1n) = 0

Subproblem 1
Set the factor '(-5 + -1n)' equal to zero and attempt to solve:

Simplifying
-5 + -1n = 0

Solving
-5 + -1n = 0

Move all terms containing n to the left, all other terms to the right.

Add '5' to each side of the equation.
-5 + 5 + -1n = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1n = 0 + 5
-1n = 0 + 5

Combine like terms: 0 + 5 = 5
-1n = 5

Divide each side by '-1'.
n = -5

Simplifying
n = -5
Subproblem 2
Set the factor '(6 + -1n)' equal to zero and attempt to solve:

Simplifying
6 + -1n = 0

Solving
6 + -1n = 0

Move all terms containing n to the left, all other terms to the right.

Add '-6' to each side of the equation.
6 + -6 + -1n = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1n = 0 + -6
-1n = 0 + -6

Combine like terms: 0 + -6 = -6
-1n = -6

Divide each side by '-1'.
n = 6

Simplifying
n = 6
Solution
n = {-5, 6}