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

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


Simplifying
x2 + 5x = 2x2 + 7x + -8

Reorder the terms:
5x + x2 = 2x2 + 7x + -8

Reorder the terms:
5x + x2 = -8 + 7x + 2x2

Solving
5x + x2 = -8 + 7x + 2x2

Solving for variable 'x'.

Reorder the terms:
8 + 5x + -7x + x2 + -2x2 = -8 + 7x + 2x2 + 8 + -7x + -2x2

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

Combine like terms: x2 + -2x2 = -1x2
8 + -2x + -1x2 = -8 + 7x + 2x2 + 8 + -7x + -2x2

Reorder the terms:
8 + -2x + -1x2 = -8 + 8 + 7x + -7x + 2x2 + -2x2

Combine like terms: -8 + 8 = 0
8 + -2x + -1x2 = 0 + 7x + -7x + 2x2 + -2x2
8 + -2x + -1x2 = 7x + -7x + 2x2 + -2x2

Combine like terms: 7x + -7x = 0
8 + -2x + -1x2 = 0 + 2x2 + -2x2
8 + -2x + -1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
8 + -2x + -1x2 = 0

Factor a trinomial.
(2 + -1x)(4 + 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 '(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
Solution
x = {2, -4}

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