180=2n^2-18n

Solution for 180=2n^2-18n equation:

Simplifying
180 = 2n2 + -18n

Reorder the terms:
180 = -18n + 2n2

Solving
180 = -18n + 2n2

Solving for variable 'n'.

Reorder the terms:
180 + 18n + -2n2 = -18n + 18n + 2n2 + -2n2

Combine like terms: -18n + 18n = 0
180 + 18n + -2n2 = 0 + 2n2 + -2n2
180 + 18n + -2n2 = 2n2 + -2n2

Combine like terms: 2n2 + -2n2 = 0
180 + 18n + -2n2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(90 + 9n + -1n2) = 0

Factor a trinomial.
2((15 + -1n)(6 + n)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(15 + -1n)' equal to zero and attempt to solve:

Simplifying
15 + -1n = 0

Solving
15 + -1n = 0

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

Add '-15' to each side of the equation.
15 + -15 + -1n = 0 + -15

Combine like terms: 15 + -15 = 0
0 + -1n = 0 + -15
-1n = 0 + -15

Combine like terms: 0 + -15 = -15
-1n = -15

Divide each side by '-1'.
n = 15

Simplifying
n = 15
Subproblem 2
Set the factor '(6 + n)' equal to zero and attempt to solve:

Simplifying
6 + n = 0

Solving
6 + n = 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 + n = 0 + -6

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

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

Simplifying
n = -6
Solution
n = {15, -6}