180=n*(n-3)

Solution for 180=n*(n-3) equation:

Simplifying
180 = n(n + -3)

Reorder the terms:
180 = n(-3 + n)
180 = (-3 * n + n * n)
180 = (-3n + n2)

Solving
180 = -3n + n2

Solving for variable 'n'.

Reorder the terms:
180 + 3n + -1n2 = -3n + 3n + n2 + -1n2

Combine like terms: -3n + 3n = 0
180 + 3n + -1n2 = 0 + n2 + -1n2
180 + 3n + -1n2 = n2 + -1n2

Combine like terms: n2 + -1n2 = 0
180 + 3n + -1n2 = 0

Factor a trinomial.
(15 + -1n)(12 + n) = 0

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 '(12 + n)' equal to zero and attempt to solve:

Simplifying
12 + n = 0

Solving
12 + n = 0

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

Add '-12' to each side of the equation.
12 + -12 + n = 0 + -12

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

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

Simplifying
n = -12
Solution
n = {15, -12}