2y^5-32z^4y=0

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Solution for 2y^5-32z^4y=0 equation: 


Simplifying
2y5 + -32z4y = 0

Reorder the terms:
-32yz4 + 2y5 = 0

Solving
-32yz4 + 2y5 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '2y'.
2y(-16z4 + y4) = 0

Factor a difference between two squares.
2y((4z2 + y2)(-4z2 + y2)) = 0

Factor a difference between two squares.
2y((4z2 + y2)((2z + y)(-2z + y))) = 0

Ignore the factor 2.

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

Simplifying
y = 0

Solving
y = 0

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

Simplifying
y = 0

Subproblem 2
Set the factor '(4z2 + y2)' equal to zero and attempt to solve:

Simplifying
4z2 + y2 = 0

Reorder the terms:
y2 + 4z2 = 0

Solving
y2 + 4z2 = 0

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

Add '-4z2' to each side of the equation.
y2 + 4z2 + -4z2 = 0 + -4z2

Combine like terms: 4z2 + -4z2 = 0
y2 + 0 = 0 + -4z2
y2 = 0 + -4z2
Remove the zero:
y2 = -4z2

Simplifying
y2 = -4z2

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 '(2z + y)' equal to zero and attempt to solve:

Simplifying
2z + y = 0

Reorder the terms:
y + 2z = 0

Solving
y + 2z = 0

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

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

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

Simplifying
y = -2z

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

Simplifying
-2z + y = 0

Reorder the terms:
y + -2z = 0

Solving
y + -2z = 0

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

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

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

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

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