x+5=x^2+7x+13

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Solution for x+5=x^2+7x+13 equation: 


Simplifying
x + 5 = x2 + 7x + 13

Reorder the terms:
5 + x = x2 + 7x + 13

Reorder the terms:
5 + x = 13 + 7x + x2

Solving
5 + x = 13 + 7x + x2

Solving for variable 'x'.

Reorder the terms:
5 + -13 + x + -7x + -1x2 = 13 + 7x + x2 + -13 + -7x + -1x2

Combine like terms: 5 + -13 = -8
-8 + x + -7x + -1x2 = 13 + 7x + x2 + -13 + -7x + -1x2

Combine like terms: x + -7x = -6x
-8 + -6x + -1x2 = 13 + 7x + x2 + -13 + -7x + -1x2

Reorder the terms:
-8 + -6x + -1x2 = 13 + -13 + 7x + -7x + x2 + -1x2

Combine like terms: 13 + -13 = 0
-8 + -6x + -1x2 = 0 + 7x + -7x + x2 + -1x2
-8 + -6x + -1x2 = 7x + -7x + x2 + -1x2

Combine like terms: 7x + -7x = 0
-8 + -6x + -1x2 = 0 + x2 + -1x2
-8 + -6x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-8 + -6x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(8 + 6x + x2) = 0

Factor a trinomial.
-1((4 + x)(2 + x)) = 0

Ignore the factor -1.

Subproblem 1
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

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 = {-4, -2}

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