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

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


Simplifying
x2 + -1x + 13 = -7x + 5

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

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

Solving
13 + -1x + x2 = 5 + -7x

Solving for variable 'x'.

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

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

Combine like terms: -1x + 7x = 6x
8 + 6x + x2 = 5 + -7x + -5 + 7x

Reorder the terms:
8 + 6x + x2 = 5 + -5 + -7x + 7x

Combine like terms: 5 + -5 = 0
8 + 6x + x2 = 0 + -7x + 7x
8 + 6x + x2 = -7x + 7x

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

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


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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