n^2+9=-6n

Solution for n^2+9=-6n equation:

Simplifying
n2 + 9 = -6n

Reorder the terms:
9 + n2 = -6n

Solving
9 + n2 = -6n

Solving for variable 'n'.

Reorder the terms:
9 + 6n + n2 = -6n + 6n

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

Factor a trinomial.
(3 + n)(3 + n) = 0

Subproblem 1
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
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 = {-3, -3}