(n*n)-n=156

Solution for (n*n)-n=156 equation:

Simplifying
(n * n) + -1n = 156

Multiply n * n
(n2) + -1n = 156
n2 + -1n = 156

Reorder the terms:
-1n + n2 = 156

Solving
-1n + n2 = 156

Solving for variable 'n'.

Reorder the terms:
-156 + -1n + n2 = 156 + -156

Combine like terms: 156 + -156 = 0
-156 + -1n + n2 = 0

Factor a trinomial.
(-12 + -1n)(13 + -1n) = 0

Subproblem 1
Set the factor '(-12 + -1n)' equal to zero and attempt to solve:

Simplifying
-12 + -1n = 0

Solving
-12 + -1n = 0

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

Add '12' to each side of the equation.
-12 + 12 + -1n = 0 + 12

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

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

Divide each side by '-1'.
n = -12

Simplifying
n = -12
Subproblem 2
Set the factor '(13 + -1n)' equal to zero and attempt to solve:

Simplifying
13 + -1n = 0

Solving
13 + -1n = 0

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

Add '-13' to each side of the equation.
13 + -13 + -1n = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -1n = 0 + -13
-1n = 0 + -13

Combine like terms: 0 + -13 = -13
-1n = -13

Divide each side by '-1'.
n = 13

Simplifying
n = 13
Solution
n = {-12, 13}