(n-4)(n+4)=n-4

Solution for (n-4)(n+4)=n-4 equation:

Simplifying
(n + -4)(n + 4) = n + -4

Reorder the terms:
(-4 + n)(n + 4) = n + -4

Reorder the terms:
(-4 + n)(4 + n) = n + -4

Multiply (-4 + n) * (4 + n)
(-4(4 + n) + n(4 + n)) = n + -4
((4 * -4 + n * -4) + n(4 + n)) = n + -4
((-16 + -4n) + n(4 + n)) = n + -4
(-16 + -4n + (4 * n + n * n)) = n + -4
(-16 + -4n + (4n + n2)) = n + -4

Combine like terms: -4n + 4n = 0
(-16 + 0 + n2) = n + -4
(-16 + n2) = n + -4

Reorder the terms:
-16 + n2 = -4 + n

Solving
-16 + n2 = -4 + n

Solving for variable 'n'.

Reorder the terms:
-16 + 4 + -1n + n2 = -4 + n + 4 + -1n

Combine like terms: -16 + 4 = -12
-12 + -1n + n2 = -4 + n + 4 + -1n

Reorder the terms:
-12 + -1n + n2 = -4 + 4 + n + -1n

Combine like terms: -4 + 4 = 0
-12 + -1n + n2 = 0 + n + -1n
-12 + -1n + n2 = n + -1n

Combine like terms: n + -1n = 0
-12 + -1n + n2 = 0

Factor a trinomial.
(-3 + -1n)(4 + -1n) = 0

Subproblem 1
Set the factor '(-3 + -1n)' equal to zero and attempt to solve:

Simplifying
-3 + -1n = 0

Solving
-3 + -1n = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1n = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1n = 0 + 3
-1n = 0 + 3

Combine like terms: 0 + 3 = 3
-1n = 3

Divide each side by '-1'.
n = -3

Simplifying
n = -3
Subproblem 2
Set the factor '(4 + -1n)' equal to zero and attempt to solve:

Simplifying
4 + -1n = 0

Solving
4 + -1n = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1n = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1n = 0 + -4
-1n = 0 + -4

Combine like terms: 0 + -4 = -4
-1n = -4

Divide each side by '-1'.
n = 4

Simplifying
n = 4
Solution
n = {-3, 4}