x+8=x^2+2x+2

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


Simplifying
x + 8 = x2 + 2x + 2

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

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

Solving
8 + x = 2 + 2x + x2

Solving for variable 'x'.

Reorder the terms:
8 + -2 + x + -2x + -1x2 = 2 + 2x + x2 + -2 + -2x + -1x2

Combine like terms: 8 + -2 = 6
6 + x + -2x + -1x2 = 2 + 2x + x2 + -2 + -2x + -1x2

Combine like terms: x + -2x = -1x
6 + -1x + -1x2 = 2 + 2x + x2 + -2 + -2x + -1x2

Reorder the terms:
6 + -1x + -1x2 = 2 + -2 + 2x + -2x + x2 + -1x2

Combine like terms: 2 + -2 = 0
6 + -1x + -1x2 = 0 + 2x + -2x + x2 + -1x2
6 + -1x + -1x2 = 2x + -2x + x2 + -1x2

Combine like terms: 2x + -2x = 0
6 + -1x + -1x2 = 0 + x2 + -1x2
6 + -1x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
6 + -1x + -1x2 = 0

Factor a trinomial.
(2 + -1x)(3 + x) = 0


Subproblem 1
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2

Subproblem 2
Set the factor '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

Solving
3 + x = 0

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

Add '-3' to each side of the equation.
3 + -3 + x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + x = 0 + -3
x = 0 + -3

Combine like terms: 0 + -3 = -3
x = -3

Simplifying
x = -3
Solution
x = {2, -3}

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