x^2+8x+31=-4x-1

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Solution for x^2+8x+31=-4x-1 equation: 


Simplifying
x2 + 8x + 31 = -4x + -1

Reorder the terms:
31 + 8x + x2 = -4x + -1

Reorder the terms:
31 + 8x + x2 = -1 + -4x

Solving
31 + 8x + x2 = -1 + -4x

Solving for variable 'x'.

Reorder the terms:
31 + 1 + 8x + 4x + x2 = -1 + -4x + 1 + 4x

Combine like terms: 31 + 1 = 32
32 + 8x + 4x + x2 = -1 + -4x + 1 + 4x

Combine like terms: 8x + 4x = 12x
32 + 12x + x2 = -1 + -4x + 1 + 4x

Reorder the terms:
32 + 12x + x2 = -1 + 1 + -4x + 4x

Combine like terms: -1 + 1 = 0
32 + 12x + x2 = 0 + -4x + 4x
32 + 12x + x2 = -4x + 4x

Combine like terms: -4x + 4x = 0
32 + 12x + x2 = 0

Factor a trinomial.
(8 + x)(4 + 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 '(4 + x)' equal to zero and attempt to solve:

Simplifying
4 + x = 0

Solving
4 + x = 0

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

Add '-4' to each side of the equation.
4 + -4 + x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + x = 0 + -4
x = 0 + -4

Combine like terms: 0 + -4 = -4
x = -4

Simplifying
x = -4
Solution
x = {-8, -4}

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