2xy(x+y)(2x-3y)=0

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Solution for 2xy(x+y)(2x-3y)=0 equation: 


Simplifying
2xy(x + y)(2x + -3y) = 0

Multiply (x + y) * (2x + -3y)
2xy(x(2x + -3y) + y(2x + -3y)) = 0
2xy((2x * x + -3y * x) + y(2x + -3y)) = 0

Reorder the terms:
2xy((-3xy + 2x2) + y(2x + -3y)) = 0
2xy((-3xy + 2x2) + y(2x + -3y)) = 0
2xy(-3xy + 2x2 + (2x * y + -3y * y)) = 0
2xy(-3xy + 2x2 + (2xy + -3y2)) = 0

Reorder the terms:
2xy(-3xy + 2xy + 2x2 + -3y2) = 0

Combine like terms: -3xy + 2xy = -1xy
2xy(-1xy + 2x2 + -3y2) = 0
(-1xy * 2xy + 2x2 * 2xy + -3y2 * 2xy) = 0

Reorder the terms:
(-6xy3 + -2x2y2 + 4x3y) = 0
(-6xy3 + -2x2y2 + 4x3y) = 0

Solving
-6xy3 + -2x2y2 + 4x3y = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2xy'.
2xy(-3y2 + -1xy + 2x2) = 0

Factor a trinomial.
2xy((-1y + -1x)(3y + -2x)) = 0

Ignore the factor 2.

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 '(-1y + -1x)' equal to zero and attempt to solve:

Simplifying
-1y + -1x = 0

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

Solving
-1x + -1y = 0

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

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

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

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

Simplifying
x = -1y

Subproblem 3
Set the factor '(3y + -2x)' equal to zero and attempt to solve:

Simplifying
3y + -2x = 0

Reorder the terms:
-2x + 3y = 0

Solving
-2x + 3y = 0

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

Add '-3y' to each side of the equation.
-2x + 3y + -3y = 0 + -3y

Combine like terms: 3y + -3y = 0
-2x + 0 = 0 + -3y
-2x = 0 + -3y
Remove the zero:
-2x = -3y

Divide each side by '-2'.
x = 1.5y

Simplifying
x = 1.5y
Solution
x = {-1y, 1.5y}

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