(n-1)n=12

Solution for (n-1)n=12 equation:

Simplifying
(n + -1) * n = 12

Reorder the terms:
(-1 + n) * n = 12

Reorder the terms for easier multiplication:
n(-1 + n) = 12
(-1 * n + n * n) = 12
(-1n + n2) = 12

Solving
-1n + n2 = 12

Solving for variable 'n'.

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

Combine like terms: 12 + -12 = 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}