2x^2-4x-8=-x^2+x

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Solution for 2x^2-4x-8=-x^2+x equation: 


Simplifying
2x2 + -4x + -8 = -1x2 + x

Reorder the terms:
-8 + -4x + 2x2 = -1x2 + x

Reorder the terms:
-8 + -4x + 2x2 = x + -1x2

Solving
-8 + -4x + 2x2 = x + -1x2

Solving for variable 'x'.

Reorder the terms:
-8 + -4x + -1x + 2x2 + x2 = x + -1x2 + -1x + x2

Combine like terms: -4x + -1x = -5x
-8 + -5x + 2x2 + x2 = x + -1x2 + -1x + x2

Combine like terms: 2x2 + x2 = 3x2
-8 + -5x + 3x2 = x + -1x2 + -1x + x2

Reorder the terms:
-8 + -5x + 3x2 = x + -1x + -1x2 + x2

Combine like terms: x + -1x = 0
-8 + -5x + 3x2 = 0 + -1x2 + x2
-8 + -5x + 3x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
-8 + -5x + 3x2 = 0

Factor a trinomial.
(-1 + -1x)(8 + -3x) = 0


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

Simplifying
-1 + -1x = 0

Solving
-1 + -1x = 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 + -1x = 0 + 1

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

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

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

Simplifying
x = -1

Subproblem 2
Set the factor '(8 + -3x)' equal to zero and attempt to solve:

Simplifying
8 + -3x = 0

Solving
8 + -3x = 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 + -3x = 0 + -8

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

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

Divide each side by '-3'.
x = 2.666666667

Simplifying
x = 2.666666667
Solution
x = {-1, 2.666666667}

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