x^2+x=-8-8x

Solution for x^2+x=-8-8x equation:

Simplifying
x2 + x = -8 + -8x

Reorder the terms:
x + x2 = -8 + -8x

Solving
x + x2 = -8 + -8x

Solving for variable 'x'.

Reorder the terms:
8 + x + 8x + x2 = -8 + -8x + 8 + 8x

Combine like terms: x + 8x = 9x
8 + 9x + x2 = -8 + -8x + 8 + 8x

Reorder the terms:
8 + 9x + x2 = -8 + 8 + -8x + 8x

Combine like terms: -8 + 8 = 0
8 + 9x + x2 = 0 + -8x + 8x
8 + 9x + x2 = -8x + 8x

Combine like terms: -8x + 8x = 0
8 + 9x + x2 = 0

Factor a trinomial.
(8 + x)(1 + x) = 0

Subproblem 1
Set the factor '(8 + x)' equal to zero and attempt to solve:

Simplifying
8 + x = 0

Solving
8 + x = 0

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

Add '-8' to each side of the equation.
8 + -8 + x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + x = 0 + -8
x = 0 + -8

Combine like terms: 0 + -8 = -8
x = -8

Simplifying
x = -8
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 = {-8, -1}