x(2x+2xy)dx+y(y-4xy)dy=0

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Solution for x(2x+2xy)dx+y(y-4xy)dy=0 equation: 


Simplifying
x(2x + 2xy) * dx + y(y + -4xy) * dy = 0

Reorder the terms for easier multiplication:
x * dx(2x + 2xy) + y(y + -4xy) * dy = 0

Multiply x * dx
dx2(2x + 2xy) + y(y + -4xy) * dy = 0
(2x * dx2 + 2xy * dx2) + y(y + -4xy) * dy = 0
(2dx3 + 2dx3y) + y(y + -4xy) * dy = 0

Reorder the terms:
2dx3 + 2dx3y + y(-4xy + y) * dy = 0

Reorder the terms for easier multiplication:
2dx3 + 2dx3y + y * dy(-4xy + y) = 0

Multiply y * dy
2dx3 + 2dx3y + dy2(-4xy + y) = 0
2dx3 + 2dx3y + (-4xy * dy2 + y * dy2) = 0
2dx3 + 2dx3y + (-4dxy3 + dy3) = 0

Reorder the terms:
-4dxy3 + 2dx3 + 2dx3y + dy3 = 0

Solving
-4dxy3 + 2dx3 + 2dx3y + dy3 = 0

Solving for variable 'd'.

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

Factor out the Greatest Common Factor (GCF), 'd'.
d(-4xy3 + 2x3 + 2x3y + y3) = 0


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

Simplifying
d = 0

Solving
d = 0

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

Simplifying
d = 0

Subproblem 2
Set the factor '(-4xy3 + 2x3 + 2x3y + y3)' equal to zero and attempt to solve:

Simplifying
-4xy3 + 2x3 + 2x3y + y3 = 0

Solving
-4xy3 + 2x3 + 2x3y + y3 = 0

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

Add '4xy3' to each side of the equation.
-4xy3 + 2x3 + 2x3y + 4xy3 + y3 = 0 + 4xy3

Reorder the terms:
-4xy3 + 4xy3 + 2x3 + 2x3y + y3 = 0 + 4xy3

Combine like terms: -4xy3 + 4xy3 = 0
0 + 2x3 + 2x3y + y3 = 0 + 4xy3
2x3 + 2x3y + y3 = 0 + 4xy3
Remove the zero:
2x3 + 2x3y + y3 = 4xy3

Add '-2x3' to each side of the equation.
2x3 + 2x3y + -2x3 + y3 = 4xy3 + -2x3

Reorder the terms:
2x3 + -2x3 + 2x3y + y3 = 4xy3 + -2x3

Combine like terms: 2x3 + -2x3 = 0
0 + 2x3y + y3 = 4xy3 + -2x3
2x3y + y3 = 4xy3 + -2x3

Add '-2x3y' to each side of the equation.
2x3y + -2x3y + y3 = 4xy3 + -2x3 + -2x3y

Combine like terms: 2x3y + -2x3y = 0
0 + y3 = 4xy3 + -2x3 + -2x3y
y3 = 4xy3 + -2x3 + -2x3y

Add '-1y3' to each side of the equation.
y3 + -1y3 = 4xy3 + -2x3 + -2x3y + -1y3

Combine like terms: y3 + -1y3 = 0
0 = 4xy3 + -2x3 + -2x3y + -1y3

Simplifying
0 = 4xy3 + -2x3 + -2x3y + -1y3

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
d = {0}

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