(x+1)(x+1)=-10x-31

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Solution for (x+1)(x+1)=-10x-31 equation: 


Simplifying
(x + 1)(x + 1) = -10x + -31

Reorder the terms:
(1 + x)(x + 1) = -10x + -31

Reorder the terms:
(1 + x)(1 + x) = -10x + -31

Multiply (1 + x) * (1 + x)
(1(1 + x) + x(1 + x)) = -10x + -31
((1 * 1 + x * 1) + x(1 + x)) = -10x + -31
((1 + 1x) + x(1 + x)) = -10x + -31
(1 + 1x + (1 * x + x * x)) = -10x + -31
(1 + 1x + (1x + x2)) = -10x + -31

Combine like terms: 1x + 1x = 2x
(1 + 2x + x2) = -10x + -31

Reorder the terms:
1 + 2x + x2 = -31 + -10x

Solving
1 + 2x + x2 = -31 + -10x

Solving for variable 'x'.

Reorder the terms:
1 + 31 + 2x + 10x + x2 = -31 + -10x + 31 + 10x

Combine like terms: 1 + 31 = 32
32 + 2x + 10x + x2 = -31 + -10x + 31 + 10x

Combine like terms: 2x + 10x = 12x
32 + 12x + x2 = -31 + -10x + 31 + 10x

Reorder the terms:
32 + 12x + x2 = -31 + 31 + -10x + 10x

Combine like terms: -31 + 31 = 0
32 + 12x + x2 = 0 + -10x + 10x
32 + 12x + x2 = -10x + 10x

Combine like terms: -10x + 10x = 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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