8x^5-2x^4+4x^2-4x=2x(4x^5-x^4+2x^2-2x)

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Solution for 8x^5-2x^4+4x^2-4x=2x(4x^5-x^4+2x^2-2x) equation: 


Simplifying
8x5 + -2x4 + 4x2 + -4x = 2x(4x5 + -1x4 + 2x2 + -2x)

Reorder the terms:
-4x + 4x2 + -2x4 + 8x5 = 2x(4x5 + -1x4 + 2x2 + -2x)

Reorder the terms:
-4x + 4x2 + -2x4 + 8x5 = 2x(-2x + 2x2 + -1x4 + 4x5)
-4x + 4x2 + -2x4 + 8x5 = (-2x * 2x + 2x2 * 2x + -1x4 * 2x + 4x5 * 2x)
-4x + 4x2 + -2x4 + 8x5 = (-4x2 + 4x3 + -2x5 + 8x6)

Solving
-4x + 4x2 + -2x4 + 8x5 = -4x2 + 4x3 + -2x5 + 8x6

Solving for variable 'x'.

Reorder the terms:
-4x + 4x2 + 4x2 + -4x3 + -2x4 + 8x5 + 2x5 + -8x6 = -4x2 + 4x3 + -2x5 + 8x6 + 4x2 + -4x3 + 2x5 + -8x6

Combine like terms: 4x2 + 4x2 = 8x2
-4x + 8x2 + -4x3 + -2x4 + 8x5 + 2x5 + -8x6 = -4x2 + 4x3 + -2x5 + 8x6 + 4x2 + -4x3 + 2x5 + -8x6

Combine like terms: 8x5 + 2x5 = 10x5
-4x + 8x2 + -4x3 + -2x4 + 10x5 + -8x6 = -4x2 + 4x3 + -2x5 + 8x6 + 4x2 + -4x3 + 2x5 + -8x6

Reorder the terms:
-4x + 8x2 + -4x3 + -2x4 + 10x5 + -8x6 = -4x2 + 4x2 + 4x3 + -4x3 + -2x5 + 2x5 + 8x6 + -8x6

Combine like terms: -4x2 + 4x2 = 0
-4x + 8x2 + -4x3 + -2x4 + 10x5 + -8x6 = 0 + 4x3 + -4x3 + -2x5 + 2x5 + 8x6 + -8x6
-4x + 8x2 + -4x3 + -2x4 + 10x5 + -8x6 = 4x3 + -4x3 + -2x5 + 2x5 + 8x6 + -8x6

Combine like terms: 4x3 + -4x3 = 0
-4x + 8x2 + -4x3 + -2x4 + 10x5 + -8x6 = 0 + -2x5 + 2x5 + 8x6 + -8x6
-4x + 8x2 + -4x3 + -2x4 + 10x5 + -8x6 = -2x5 + 2x5 + 8x6 + -8x6

Combine like terms: -2x5 + 2x5 = 0
-4x + 8x2 + -4x3 + -2x4 + 10x5 + -8x6 = 0 + 8x6 + -8x6
-4x + 8x2 + -4x3 + -2x4 + 10x5 + -8x6 = 8x6 + -8x6

Combine like terms: 8x6 + -8x6 = 0
-4x + 8x2 + -4x3 + -2x4 + 10x5 + -8x6 = 0

Factor out the Greatest Common Factor (GCF), '2x'.
2x(-2 + 4x + -2x2 + -1x3 + 5x4 + -4x5) = 0

Ignore the factor 2.

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(-2 + 4x + -2x2 + -1x3 + 5x4 + -4x5)' equal to zero and attempt to solve:

Simplifying
-2 + 4x + -2x2 + -1x3 + 5x4 + -4x5 = 0

Solving
-2 + 4x + -2x2 + -1x3 + 5x4 + -4x5 = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
x = {0}

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