-2x+1=x^2+2x+5

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Solution for -2x+1=x^2+2x+5 equation: 


Simplifying
-2x + 1 = x2 + 2x + 5

Reorder the terms:
1 + -2x = x2 + 2x + 5

Reorder the terms:
1 + -2x = 5 + 2x + x2

Solving
1 + -2x = 5 + 2x + x2

Solving for variable 'x'.

Reorder the terms:
1 + -5 + -2x + -2x + -1x2 = 5 + 2x + x2 + -5 + -2x + -1x2

Combine like terms: 1 + -5 = -4
-4 + -2x + -2x + -1x2 = 5 + 2x + x2 + -5 + -2x + -1x2

Combine like terms: -2x + -2x = -4x
-4 + -4x + -1x2 = 5 + 2x + x2 + -5 + -2x + -1x2

Reorder the terms:
-4 + -4x + -1x2 = 5 + -5 + 2x + -2x + x2 + -1x2

Combine like terms: 5 + -5 = 0
-4 + -4x + -1x2 = 0 + 2x + -2x + x2 + -1x2
-4 + -4x + -1x2 = 2x + -2x + x2 + -1x2

Combine like terms: 2x + -2x = 0
-4 + -4x + -1x2 = 0 + x2 + -1x2
-4 + -4x + -1x2 = x2 + -1x2

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

Factor out the Greatest Common Factor (GCF), '-1'.
-1(4 + 4x + x2) = 0

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

Ignore the factor -1.

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

Simplifying
2 + x = 0

Solving
2 + x = 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 + x = 0 + -2

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

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

Simplifying
x = -2

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

Simplifying
2 + x = 0

Solving
2 + x = 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 + x = 0 + -2

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

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

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

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