x^2-5x+7=-8x+5

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Solution for x^2-5x+7=-8x+5 equation: 


Simplifying
x2 + -5x + 7 = -8x + 5

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

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

Solving
7 + -5x + x2 = 5 + -8x

Solving for variable 'x'.

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

Combine like terms: 7 + -5 = 2
2 + -5x + 8x + x2 = 5 + -8x + -5 + 8x

Combine like terms: -5x + 8x = 3x
2 + 3x + x2 = 5 + -8x + -5 + 8x

Reorder the terms:
2 + 3x + x2 = 5 + -5 + -8x + 8x

Combine like terms: 5 + -5 = 0
2 + 3x + x2 = 0 + -8x + 8x
2 + 3x + x2 = -8x + 8x

Combine like terms: -8x + 8x = 0
2 + 3x + x2 = 0

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


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 '(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 = {-2, -1}

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