n^2-n+12=6n

Solution for n^2-n+12=6n equation:

Simplifying
n2 + -1n + 12 = 6n

Reorder the terms:
12 + -1n + n2 = 6n

Solving
12 + -1n + n2 = 6n

Solving for variable 'n'.

Reorder the terms:
12 + -1n + -6n + n2 = 6n + -6n

Combine like terms: -1n + -6n = -7n
12 + -7n + n2 = 6n + -6n

Combine like terms: 6n + -6n = 0
12 + -7n + 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}