z^6+4z^5y-32z^4y^2=

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Solution for z^6+4z^5y-32z^4y^2= equation: 


Simplifying
z6 + 4z5y + -32z4y2 = 0

Reorder the terms:
4yz5 + -32y2z4 + z6 = 0

Solving
4yz5 + -32y2z4 + z6 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), 'z4'.
z4(4yz + -32y2 + z2) = 0

Factor a trinomial.
z4((-8y + -1z)(4y + -1z)) = 0


Subproblem 1
Set the factor 'z4' equal to zero and attempt to solve:

Simplifying
z4 = 0

Solving
z4 = 0

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

Add '-1z4' to each side of the equation.
z4 + -1z4 = 0 + -1z4
Remove the zero:
0 = -1z4

Simplifying
0 = -1z4

The solution to this equation could not be determined.

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

Subproblem 2
Set the factor '(-8y + -1z)' equal to zero and attempt to solve:

Simplifying
-8y + -1z = 0

Solving
-8y + -1z = 0

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

Add 'z' to each side of the equation.
-8y + -1z + z = 0 + z

Combine like terms: -1z + z = 0
-8y + 0 = 0 + z
-8y = 0 + z
Remove the zero:
-8y = z

Divide each side by '-8'.
y = -0.125z

Simplifying
y = -0.125z

Subproblem 3
Set the factor '(4y + -1z)' equal to zero and attempt to solve:

Simplifying
4y + -1z = 0

Solving
4y + -1z = 0

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

Add 'z' to each side of the equation.
4y + -1z + z = 0 + z

Combine like terms: -1z + z = 0
4y + 0 = 0 + z
4y = 0 + z
Remove the zero:
4y = z

Divide each side by '4'.
y = 0.25z

Simplifying
y = 0.25z
Solution
y = {-0.125z, 0.25z}

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