x^2+2x=-4x-5

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Solution for x^2+2x=-4x-5 equation: 


Simplifying
x2 + 2x = -4x + -5

Reorder the terms:
2x + x2 = -4x + -5

Reorder the terms:
2x + x2 = -5 + -4x

Solving
2x + x2 = -5 + -4x

Solving for variable 'x'.

Reorder the terms:
5 + 2x + 4x + x2 = -5 + -4x + 5 + 4x

Combine like terms: 2x + 4x = 6x
5 + 6x + x2 = -5 + -4x + 5 + 4x

Reorder the terms:
5 + 6x + x2 = -5 + 5 + -4x + 4x

Combine like terms: -5 + 5 = 0
5 + 6x + x2 = 0 + -4x + 4x
5 + 6x + x2 = -4x + 4x

Combine like terms: -4x + 4x = 0
5 + 6x + x2 = 0

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


Subproblem 1
Set the factor '(5 + x)' equal to zero and attempt to solve:

Simplifying
5 + x = 0

Solving
5 + x = 0

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

Add '-5' to each side of the equation.
5 + -5 + x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + x = 0 + -5
x = 0 + -5

Combine like terms: 0 + -5 = -5
x = -5

Simplifying
x = -5

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 = {-5, -1}

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