(x*x)+6x=-9

Solution for (x*x)+6x=-9 equation:

Simplifying
(x * x) + 6x = -9

Multiply x * x
(x2) + 6x = -9
x2 + 6x = -9

Reorder the terms:
6x + x2 = -9

Solving
6x + x2 = -9

Solving for variable 'x'.

Reorder the terms:
9 + 6x + x2 = -9 + 9

Combine like terms: -9 + 9 = 0
9 + 6x + x2 = 0

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

Subproblem 1
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
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 = {-3, -3}