2x^2-x=x^2+2x+40

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Solution for 2x^2-x=x^2+2x+40 equation: 


Simplifying
2x2 + -1x = x2 + 2x + 40

Reorder the terms:
-1x + 2x2 = x2 + 2x + 40

Reorder the terms:
-1x + 2x2 = 40 + 2x + x2

Solving
-1x + 2x2 = 40 + 2x + x2

Solving for variable 'x'.

Reorder the terms:
-40 + -1x + -2x + 2x2 + -1x2 = 40 + 2x + x2 + -40 + -2x + -1x2

Combine like terms: -1x + -2x = -3x
-40 + -3x + 2x2 + -1x2 = 40 + 2x + x2 + -40 + -2x + -1x2

Combine like terms: 2x2 + -1x2 = 1x2
-40 + -3x + 1x2 = 40 + 2x + x2 + -40 + -2x + -1x2

Reorder the terms:
-40 + -3x + 1x2 = 40 + -40 + 2x + -2x + x2 + -1x2

Combine like terms: 40 + -40 = 0
-40 + -3x + 1x2 = 0 + 2x + -2x + x2 + -1x2
-40 + -3x + 1x2 = 2x + -2x + x2 + -1x2

Combine like terms: 2x + -2x = 0
-40 + -3x + 1x2 = 0 + x2 + -1x2
-40 + -3x + 1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-40 + -3x + 1x2 = 0

Factor a trinomial.
(-5 + -1x)(8 + -1x) = 0


Subproblem 1
Set the factor '(-5 + -1x)' equal to zero and attempt to solve:

Simplifying
-5 + -1x = 0

Solving
-5 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '5' to each side of the equation.
-5 + 5 + -1x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1x = 0 + 5
-1x = 0 + 5

Combine like terms: 0 + 5 = 5
-1x = 5

Divide each side by '-1'.
x = -5

Simplifying
x = -5

Subproblem 2
Set the factor '(8 + -1x)' equal to zero and attempt to solve:

Simplifying
8 + -1x = 0

Solving
8 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-8' to each side of the equation.
8 + -8 + -1x = 0 + -8

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

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

Divide each side by '-1'.
x = 8

Simplifying
x = 8
Solution
x = {-5, 8}

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