n(n-1)=8n+36

Solution for n(n-1)=8n+36 equation:

Simplifying
n(n + -1) = 8n + 36

Reorder the terms:
n(-1 + n) = 8n + 36
(-1 * n + n * n) = 8n + 36
(-1n + n2) = 8n + 36

Reorder the terms:
-1n + n2 = 36 + 8n

Solving
-1n + n2 = 36 + 8n

Solving for variable 'n'.

Reorder the terms:
-36 + -1n + -8n + n2 = 36 + 8n + -36 + -8n

Combine like terms: -1n + -8n = -9n
-36 + -9n + n2 = 36 + 8n + -36 + -8n

Reorder the terms:
-36 + -9n + n2 = 36 + -36 + 8n + -8n

Combine like terms: 36 + -36 = 0
-36 + -9n + n2 = 0 + 8n + -8n
-36 + -9n + n2 = 8n + -8n

Combine like terms: 8n + -8n = 0
-36 + -9n + n2 = 0

Factor a trinomial.
(-3 + -1n)(12 + -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 '(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
Solution
n = {-3, 12}