3x(x-y)3xy(x+y)=

Solution for 3x(x-y)3xy(x+y)= equation:

Simplifying
3x(x + -1y) * 3xy(x + y) = 0

Reorder the terms for easier multiplication:
3 * 3x * xy(x + -1y)(x + y) = 0

Multiply 3 * 3
9x * xy(x + -1y)(x + y) = 0

Multiply x * xy
9x2y(x + -1y)(x + y) = 0

Multiply (x + -1y) * (x + y)
9x2y(x(x + y) + -1y * (x + y)) = 0
9x2y((x * x + y * x) + -1y * (x + y)) = 0

Reorder the terms:
9x2y((xy + x2) + -1y * (x + y)) = 0
9x2y((xy + x2) + -1y * (x + y)) = 0
9x2y(xy + x2 + (x * -1y + y * -1y)) = 0
9x2y(xy + x2 + (-1xy + -1y2)) = 0

Reorder the terms:
9x2y(xy + -1xy + x2 + -1y2) = 0

Combine like terms: xy + -1xy = 0
9x2y(0 + x2 + -1y2) = 0
9x2y(x2 + -1y2) = 0
(x2 * 9x2y + -1y2 * 9x2y) = 0

Reorder the terms:
(-9x2y3 + 9x4y) = 0
(-9x2y3 + 9x4y) = 0

Solving
-9x2y3 + 9x4y = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '9x2y'.
9x2y(-1y2 + x2) = 0

Factor a difference between two squares.
9x2y((y + x)(-1y + x)) = 0

Ignore the factor 9.
Subproblem 1
Set the factor 'x2y' equal to zero and attempt to solve:

Simplifying
x2y = 0

Solving
x2y = 0

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

Simplifying
x2y = 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 '(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 3
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}