x^5y^2-xy^6=

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Solution for x^5y^2-xy^6= equation: 


Simplifying
x5y2 + -1xy6 = 0

Reorder the terms:
-1xy6 + x5y2 = 0

Solving
-1xy6 + x5y2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'xy2'.
xy2(-1y4 + x4) = 0

Factor a difference between two squares.
xy2((y2 + x2)(-1y2 + x2)) = 0

Factor a difference between two squares.
xy2((y2 + x2)((y + x)(-1y + x))) = 0


Subproblem 1
Set the factor 'xy2' equal to zero and attempt to solve:

Simplifying
xy2 = 0

Solving
xy2 = 0

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

Simplifying
xy2 = 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 '(y2 + x2)' equal to zero and attempt to solve:

Simplifying
y2 + x2 = 0

Reorder the terms:
x2 + y2 = 0

Solving
x2 + y2 = 0

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

Add '-1y2' to each side of the equation.
x2 + y2 + -1y2 = 0 + -1y2

Combine like terms: y2 + -1y2 = 0
x2 + 0 = 0 + -1y2
x2 = 0 + -1y2
Remove the zero:
x2 = -1y2

Simplifying
x2 = -1y2

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

Simplifying
y + x = 0

Reorder the terms:
x + y = 0

Solving
x + y = 0

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

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

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

Simplifying
x = -1y

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

Simplifying
-1y + x = 0

Reorder the terms:
x + -1y = 0

Solving
x + -1y = 0

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

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

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

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

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