32xy^4-2x^5=0

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Solution for 32xy^4-2x^5=0 equation: 


Simplifying
32xy4 + -2x5 = 0

Solving
32xy4 + -2x5 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x'.
2x(16y4 + -1x4) = 0

Factor a difference between two squares.
2x((4y2 + x2)(4y2 + -1x2)) = 0

Factor a difference between two squares.
2x((4y2 + x2)((2y + x)(2y + -1x))) = 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 '(4y2 + x2)' equal to zero and attempt to solve:

Simplifying
4y2 + x2 = 0

Reorder the terms:
x2 + 4y2 = 0

Solving
x2 + 4y2 = 0

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

Add '-4y2' to each side of the equation.
x2 + 4y2 + -4y2 = 0 + -4y2

Combine like terms: 4y2 + -4y2 = 0
x2 + 0 = 0 + -4y2
x2 = 0 + -4y2
Remove the zero:
x2 = -4y2

Simplifying
x2 = -4y2

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

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

Simplifying
2y + x = 0

Reorder the terms:
x + 2y = 0

Solving
x + 2y = 0

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

Add '-2y' to each side of the equation.
x + 2y + -2y = 0 + -2y

Combine like terms: 2y + -2y = 0
x + 0 = 0 + -2y
x = 0 + -2y
Remove the zero:
x = -2y

Simplifying
x = -2y

Subproblem 4
Set the factor '(2y + -1x)' equal to zero and attempt to solve:

Simplifying
2y + -1x = 0

Reorder the terms:
-1x + 2y = 0

Solving
-1x + 2y = 0

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

Add '-2y' to each side of the equation.
-1x + 2y + -2y = 0 + -2y

Combine like terms: 2y + -2y = 0
-1x + 0 = 0 + -2y
-1x = 0 + -2y
Remove the zero:
-1x = -2y

Divide each side by '-1'.
x = 2y

Simplifying
x = 2y
Solution
x = {0, -2y, 2y}

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