x^2+10x+5=2x-2

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Solution for x^2+10x+5=2x-2 equation: 


Simplifying
x2 + 10x + 5 = 2x + -2

Reorder the terms:
5 + 10x + x2 = 2x + -2

Reorder the terms:
5 + 10x + x2 = -2 + 2x

Solving
5 + 10x + x2 = -2 + 2x

Solving for variable 'x'.

Reorder the terms:
5 + 2 + 10x + -2x + x2 = -2 + 2x + 2 + -2x

Combine like terms: 5 + 2 = 7
7 + 10x + -2x + x2 = -2 + 2x + 2 + -2x

Combine like terms: 10x + -2x = 8x
7 + 8x + x2 = -2 + 2x + 2 + -2x

Reorder the terms:
7 + 8x + x2 = -2 + 2 + 2x + -2x

Combine like terms: -2 + 2 = 0
7 + 8x + x2 = 0 + 2x + -2x
7 + 8x + x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
7 + 8x + x2 = 0

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


Subproblem 1
Set the factor '(7 + x)' equal to zero and attempt to solve:

Simplifying
7 + x = 0

Solving
7 + x = 0

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

Add '-7' to each side of the equation.
7 + -7 + x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + x = 0 + -7
x = 0 + -7

Combine like terms: 0 + -7 = -7
x = -7

Simplifying
x = -7

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 = {-7, -1}

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