n^2-2n+n-2-54=0

Solution for n^2-2n+n-2-54=0 equation:

Simplifying
n2 + -2n + n + -2 + -54 = 0

Reorder the terms:
-2 + -54 + -2n + n + n2 = 0

Combine like terms: -2 + -54 = -56
-56 + -2n + n + n2 = 0

Combine like terms: -2n + n = -1n
-56 + -1n + n2 = 0

Solving
-56 + -1n + n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(-7 + -1n)(8 + -1n) = 0

Subproblem 1
Set the factor '(-7 + -1n)' equal to zero and attempt to solve:

Simplifying
-7 + -1n = 0

Solving
-7 + -1n = 0

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

Add '7' to each side of the equation.
-7 + 7 + -1n = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1n = 0 + 7
-1n = 0 + 7

Combine like terms: 0 + 7 = 7
-1n = 7

Divide each side by '-1'.
n = -7

Simplifying
n = -7
Subproblem 2
Set the factor '(8 + -1n)' equal to zero and attempt to solve:

Simplifying
8 + -1n = 0

Solving
8 + -1n = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1n = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1n = 0 + -8
-1n = 0 + -8

Combine like terms: 0 + -8 = -8
-1n = -8

Divide each side by '-1'.
n = 8

Simplifying
n = 8
Solution
n = {-7, 8}