-n^2-15n+72=-9n

Solution for -n^2-15n+72=-9n equation:

Simplifying
-1n2 + -15n + 72 = -9n

Reorder the terms:
72 + -15n + -1n2 = -9n

Solving
72 + -15n + -1n2 = -9n

Solving for variable 'n'.

Reorder the terms:
72 + -15n + 9n + -1n2 = -9n + 9n

Combine like terms: -15n + 9n = -6n
72 + -6n + -1n2 = -9n + 9n

Combine like terms: -9n + 9n = 0
72 + -6n + -1n2 = 0

Factor a trinomial.
(6 + -1n)(12 + n) = 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 + 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 = {6, -12}