n^2=8n-12

Solution for n^2=8n-12 equation:

Simplifying
n2 = 8n + -12

Reorder the terms:
n2 = -12 + 8n

Solving
n2 = -12 + 8n

Solving for variable 'n'.

Reorder the terms:
12 + -8n + n2 = -12 + 8n + 12 + -8n

Reorder the terms:
12 + -8n + n2 = -12 + 12 + 8n + -8n

Combine like terms: -12 + 12 = 0
12 + -8n + n2 = 0 + 8n + -8n
12 + -8n + n2 = 8n + -8n

Combine like terms: 8n + -8n = 0
12 + -8n + n2 = 0

Factor a trinomial.
(2 + -1n)(6 + -1n) = 0

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

Simplifying
2 + -1n = 0

Solving
2 + -1n = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1n = 0 + -2

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

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

Divide each side by '-1'.
n = 2

Simplifying
n = 2
Subproblem 2
Set the factor '(6 + -1n)' equal to zero and attempt to solve:

Simplifying
6 + -1n = 0

Solving
6 + -1n = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1n = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1n = 0 + -6
-1n = 0 + -6

Combine like terms: 0 + -6 = -6
-1n = -6

Divide each side by '-1'.
n = 6

Simplifying
n = 6
Solution
n = {2, 6}