9x=-x^2-18

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

Simplifying
9x = -1x2 + -18

Reorder the terms:
9x = -18 + -1x2

Solving
9x = -18 + -1x2

Solving for variable 'x'.

Reorder the terms:
18 + 9x + x2 = -18 + -1x2 + 18 + x2

Reorder the terms:
18 + 9x + x2 = -18 + 18 + -1x2 + x2

Combine like terms: -18 + 18 = 0
18 + 9x + x2 = 0 + -1x2 + x2
18 + 9x + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
18 + 9x + x2 = 0

Factor a trinomial.
(6 + x)(3 + x) = 0

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

Simplifying
6 + x = 0

Solving
6 + x = 0

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

Add '-6' to each side of the equation.
6 + -6 + x = 0 + -6

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

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

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

Simplifying
3 + x = 0

Solving
3 + x = 0

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

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

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

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

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