3y(x+y)*4x(x-y)=

Solution for 3y(x+y)*4x(x-y)= equation:

Simplifying
3y(x + y) * 4x(x + -1y) = 0

Reorder the terms for easier multiplication:
3 * 4y * x(x + y)(x + -1y) = 0

Multiply 3 * 4
12y * x(x + y)(x + -1y) = 0

Multiply y * x
12xy(x + y)(x + -1y) = 0

Multiply (x + y) * (x + -1y)
12xy(x(x + -1y) + y(x + -1y)) = 0
12xy((x * x + -1y * x) + y(x + -1y)) = 0

Reorder the terms:
12xy((-1xy + x2) + y(x + -1y)) = 0
12xy((-1xy + x2) + y(x + -1y)) = 0
12xy(-1xy + x2 + (x * y + -1y * y)) = 0
12xy(-1xy + x2 + (xy + -1y2)) = 0

Reorder the terms:
12xy(-1xy + xy + x2 + -1y2) = 0

Combine like terms: -1xy + xy = 0
12xy(0 + x2 + -1y2) = 0
12xy(x2 + -1y2) = 0
(x2 * 12xy + -1y2 * 12xy) = 0

Reorder the terms:
(-12xy3 + 12x3y) = 0
(-12xy3 + 12x3y) = 0

Solving
-12xy3 + 12x3y = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '12xy'.
12xy(-1y2 + x2) = 0

Factor a difference between two squares.
12xy((y + x)(-1y + x)) = 0

Ignore the factor 12.
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 '(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}