243x^5y-3xy^5=

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Solution for 243x^5y-3xy^5= equation: 


Simplifying
243x5y + -3xy5 = 0

Reorder the terms:
-3xy5 + 243x5y = 0

Solving
-3xy5 + 243x5y = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3xy'.
3xy(-1y4 + 81x4) = 0

Factor a difference between two squares.
3xy((y2 + 9x2)(-1y2 + 9x2)) = 0

Factor a difference between two squares.
3xy((y2 + 9x2)((y + 3x)(-1y + 3x))) = 0

Ignore the factor 3.

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

Simplifying
xy = 0

Solving
xy = 0

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

Simplifying
xy = 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 + 9x2)' equal to zero and attempt to solve:

Simplifying
y2 + 9x2 = 0

Reorder the terms:
9x2 + y2 = 0

Solving
9x2 + y2 = 0

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

Add '-1y2' to each side of the equation.
9x2 + y2 + -1y2 = 0 + -1y2

Combine like terms: y2 + -1y2 = 0
9x2 + 0 = 0 + -1y2
9x2 = 0 + -1y2
Remove the zero:
9x2 = -1y2

Divide each side by '9'.
x2 = -0.1111111111y2

Simplifying
x2 = -0.1111111111y2

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 + 3x)' equal to zero and attempt to solve:

Simplifying
y + 3x = 0

Reorder the terms:
3x + y = 0

Solving
3x + y = 0

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

Add '-1y' to each side of the equation.
3x + y + -1y = 0 + -1y

Combine like terms: y + -1y = 0
3x + 0 = 0 + -1y
3x = 0 + -1y
Remove the zero:
3x = -1y

Divide each side by '3'.
x = -0.3333333333y

Simplifying
x = -0.3333333333y

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

Simplifying
-1y + 3x = 0

Reorder the terms:
3x + -1y = 0

Solving
3x + -1y = 0

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

Add 'y' to each side of the equation.
3x + -1y + y = 0 + y

Combine like terms: -1y + y = 0
3x + 0 = 0 + y
3x = 0 + y
Remove the zero:
3x = y

Divide each side by '3'.
x = 0.3333333333y

Simplifying
x = 0.3333333333y
Solution
x = {-0.3333333333y, 0.3333333333y}

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