9n-n^2=18

Solution for 9n-n^2=18 equation:

Simplifying
9n + -1n2 = 18

Solving
9n + -1n2 = 18

Solving for variable 'n'.

Reorder the terms:
-18 + 9n + -1n2 = 18 + -18

Combine like terms: 18 + -18 = 0
-18 + 9n + -1n2 = 0

Factor a trinomial.
(-6 + n)(3 + -1n) = 0

Subproblem 1
Set the factor '(-6 + n)' equal to zero and attempt to solve:

Simplifying
-6 + n = 0

Solving
-6 + n = 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 + n = 0 + 6

Combine like terms: -6 + 6 = 0
0 + n = 0 + 6
n = 0 + 6

Combine like terms: 0 + 6 = 6
n = 6

Simplifying
n = 6
Subproblem 2
Set the factor '(3 + -1n)' equal to zero and attempt to solve:

Simplifying
3 + -1n = 0

Solving
3 + -1n = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1n = 0 + -3

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

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

Divide each side by '-1'.
n = 3

Simplifying
n = 3
Solution
n = {6, 3}