6n^2-180=6n

Solution for 6n^2-180=6n equation:

Simplifying
6n2 + -180 = 6n

Reorder the terms:
-180 + 6n2 = 6n

Solving
-180 + 6n2 = 6n

Solving for variable 'n'.

Reorder the terms:
-180 + -6n + 6n2 = 6n + -6n

Combine like terms: 6n + -6n = 0
-180 + -6n + 6n2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(-30 + -1n + n2) = 0

Factor a trinomial.
6((-5 + -1n)(6 + -1n)) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(-5 + -1n)' equal to zero and attempt to solve:

Simplifying
-5 + -1n = 0

Solving
-5 + -1n = 0

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

Add '5' to each side of the equation.
-5 + 5 + -1n = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1n = 0 + 5
-1n = 0 + 5

Combine like terms: 0 + 5 = 5
-1n = 5

Divide each side by '-1'.
n = -5

Simplifying
n = -5
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 = {-5, 6}