0=n^2-18n+72

Solution for 0=n^2-18n+72 equation:

Simplifying
0 = n2 + -18n + 72

Reorder the terms:
0 = 72 + -18n + n2

Solving
0 = 72 + -18n + n2

Solving for variable 'n'.

Combine like terms: 0 + -72 = -72
-72 + 18n + -1n2 = 72 + -18n + n2 + -72 + 18n + -1n2

Reorder the terms:
-72 + 18n + -1n2 = 72 + -72 + -18n + 18n + n2 + -1n2

Combine like terms: 72 + -72 = 0
-72 + 18n + -1n2 = 0 + -18n + 18n + n2 + -1n2
-72 + 18n + -1n2 = -18n + 18n + n2 + -1n2

Combine like terms: -18n + 18n = 0
-72 + 18n + -1n2 = 0 + n2 + -1n2
-72 + 18n + -1n2 = n2 + -1n2

Combine like terms: n2 + -1n2 = 0
-72 + 18n + -1n2 = 0

Factor a trinomial.
(-12 + n)(6 + -1n) = 0

Subproblem 1
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
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 = {12, 6}