x^2+6x=-6-x

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

Simplifying
x2 + 6x = -6 + -1x

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

Solving
6x + x2 = -6 + -1x

Solving for variable 'x'.

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

Combine like terms: 6x + x = 7x
6 + 7x + x2 = -6 + -1x + 6 + x

Reorder the terms:
6 + 7x + x2 = -6 + 6 + -1x + x

Combine like terms: -6 + 6 = 0
6 + 7x + x2 = 0 + -1x + x
6 + 7x + x2 = -1x + x

Combine like terms: -1x + x = 0
6 + 7x + x2 = 0

Factor a trinomial.
(6 + x)(1 + 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 '(1 + x)' equal to zero and attempt to solve:

Simplifying
1 + x = 0

Solving
1 + x = 0

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

Add '-1' to each side of the equation.
1 + -1 + x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + x = 0 + -1
x = 0 + -1

Combine like terms: 0 + -1 = -1
x = -1

Simplifying
x = -1
Solution
x = {-6, -1}