x^2+6x+6=x

Solution for x^2+6x+6=x equation:

Simplifying
x2 + 6x + 6 = x

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

Solving
6 + 6x + x2 = x

Solving for variable 'x'.

Reorder the terms:
6 + 6x + -1x + x2 = x + -1x

Combine like terms: 6x + -1x = 5x
6 + 5x + x2 = x + -1x

Combine like terms: x + -1x = 0
6 + 5x + x2 = 0

Factor a trinomial.
(3 + x)(2 + 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 '(2 + x)' equal to zero and attempt to solve:

Simplifying
2 + x = 0

Solving
2 + x = 0

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

Add '-2' to each side of the equation.
2 + -2 + x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + x = 0 + -2
x = 0 + -2

Combine like terms: 0 + -2 = -2
x = -2

Simplifying
x = -2
Solution
x = {-3, -2}