-9n-1=n^2+17

Solution for -9n-1=n^2+17 equation:

Simplifying
-9n + -1 = n2 + 17

Reorder the terms:
-1 + -9n = n2 + 17

Reorder the terms:
-1 + -9n = 17 + n2

Solving
-1 + -9n = 17 + n2

Solving for variable 'n'.

Reorder the terms:
-1 + -17 + -9n + -1n2 = 17 + n2 + -17 + -1n2

Combine like terms: -1 + -17 = -18
-18 + -9n + -1n2 = 17 + n2 + -17 + -1n2

Reorder the terms:
-18 + -9n + -1n2 = 17 + -17 + n2 + -1n2

Combine like terms: 17 + -17 = 0
-18 + -9n + -1n2 = 0 + n2 + -1n2
-18 + -9n + -1n2 = n2 + -1n2

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

Factor out the Greatest Common Factor (GCF), '-1'.
-1(18 + 9n + n2) = 0

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

Ignore the factor -1.
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 + n)' equal to zero and attempt to solve:

Simplifying
3 + n = 0

Solving
3 + n = 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 + n = 0 + -3

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

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

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