180=2n(n-1)

Solution for 180=2n(n-1) equation:

Simplifying
180 = 2n(n + -1)

Reorder the terms:
180 = 2n(-1 + n)
180 = (-1 * 2n + n * 2n)
180 = (-2n + 2n2)

Solving
180 = -2n + 2n2

Solving for variable 'n'.

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

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

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

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

Factor a trinomial.
2((10 + -1n)(9 + n)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(10 + -1n)' equal to zero and attempt to solve:

Simplifying
10 + -1n = 0

Solving
10 + -1n = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1n = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1n = 0 + -10
-1n = 0 + -10

Combine like terms: 0 + -10 = -10
-1n = -10

Divide each side by '-1'.
n = 10

Simplifying
n = 10
Subproblem 2
Set the factor '(9 + n)' equal to zero and attempt to solve:

Simplifying
9 + n = 0

Solving
9 + n = 0

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

Add '-9' to each side of the equation.
9 + -9 + n = 0 + -9

Combine like terms: 9 + -9 = 0
0 + n = 0 + -9
n = 0 + -9

Combine like terms: 0 + -9 = -9
n = -9

Simplifying
n = -9
Solution
n = {10, -9}