0=-64x^4+128x^3-80x^2+15x

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Solution for 0=-64x^4+128x^3-80x^2+15x equation: 


Simplifying
0 = -64x4 + 128x3 + -80x2 + 15x

Reorder the terms:
0 = 15x + -80x2 + 128x3 + -64x4

Solving
0 = 15x + -80x2 + 128x3 + -64x4

Solving for variable 'x'.
Remove the zero:
-15x + 80x2 + -128x3 + 64x4 = 15x + -80x2 + 128x3 + -64x4 + -15x + 80x2 + -128x3 + 64x4

Reorder the terms:
-15x + 80x2 + -128x3 + 64x4 = 15x + -15x + -80x2 + 80x2 + 128x3 + -128x3 + -64x4 + 64x4

Combine like terms: 15x + -15x = 0
-15x + 80x2 + -128x3 + 64x4 = 0 + -80x2 + 80x2 + 128x3 + -128x3 + -64x4 + 64x4
-15x + 80x2 + -128x3 + 64x4 = -80x2 + 80x2 + 128x3 + -128x3 + -64x4 + 64x4

Combine like terms: -80x2 + 80x2 = 0
-15x + 80x2 + -128x3 + 64x4 = 0 + 128x3 + -128x3 + -64x4 + 64x4
-15x + 80x2 + -128x3 + 64x4 = 128x3 + -128x3 + -64x4 + 64x4

Combine like terms: 128x3 + -128x3 = 0
-15x + 80x2 + -128x3 + 64x4 = 0 + -64x4 + 64x4
-15x + 80x2 + -128x3 + 64x4 = -64x4 + 64x4

Combine like terms: -64x4 + 64x4 = 0
-15x + 80x2 + -128x3 + 64x4 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-15 + 80x + -128x2 + 64x3) = 0


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 '(-15 + 80x + -128x2 + 64x3)' equal to zero and attempt to solve:

Simplifying
-15 + 80x + -128x2 + 64x3 = 0

Solving
-15 + 80x + -128x2 + 64x3 = 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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