z^7y^3=zy^5

Solution for z^7y^3=zy^5 equation:

Simplifying
z7y3 = zy5

Solving
y3z7 = y5z

Solving for variable 'y'.

Combine like terms: y5z + -1y5z = 0
y3z7 + -1y5z = 0

Factor out the Greatest Common Factor (GCF), 'y3z'.
y3z(z6 + -1y2) = 0

Factor a difference between two squares.
y3z((z3 + y)(z3 + -1y)) = 0

Subproblem 1
Set the factor 'y3z' equal to zero and attempt to solve:

Simplifying
y3z = 0

Solving
y3z = 0

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

Simplifying
y3z = 0

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 '(z3 + y)' equal to zero and attempt to solve:

Simplifying
z3 + y = 0

Reorder the terms:
y + z3 = 0

Solving
y + z3 = 0

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

Add '-1z3' to each side of the equation.
y + z3 + -1z3 = 0 + -1z3

Combine like terms: z3 + -1z3 = 0
y + 0 = 0 + -1z3
y = 0 + -1z3
Remove the zero:
y = -1z3

Simplifying
y = -1z3
Subproblem 3
Set the factor '(z3 + -1y)' equal to zero and attempt to solve:

Simplifying
z3 + -1y = 0

Reorder the terms:
-1y + z3 = 0

Solving
-1y + z3 = 0

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

Add '-1z3' to each side of the equation.
-1y + z3 + -1z3 = 0 + -1z3

Combine like terms: z3 + -1z3 = 0
-1y + 0 = 0 + -1z3
-1y = 0 + -1z3
Remove the zero:
-1y = -1z3

Divide each side by '-1'.
y = z3

Simplifying
y = z3
Solution
y = {-1z3, z3}