n(n-18)=-72

Solution for n(n-18)=-72 equation:

Simplifying
n(n + -18) = -72

Reorder the terms:
n(-18 + n) = -72
(-18 * n + n * n) = -72
(-18n + n2) = -72

Solving
-18n + n2 = -72

Solving for variable 'n'.

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

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

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

Subproblem 1
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
Subproblem 2
Set the factor '(12 + -1n)' equal to zero and attempt to solve:

Simplifying
12 + -1n = 0

Solving
12 + -1n = 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 + -1n = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -1n = 0 + -12
-1n = 0 + -12

Combine like terms: 0 + -12 = -12
-1n = -12

Divide each side by '-1'.
n = 12

Simplifying
n = 12
Solution
n = {6, 12}