(4x^3y-4y^3)dy-(6x^5+6x^2y^2)dx=0

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Solution for (4x^3y-4y^3)dy-(6x^5+6x^2y^2)dx=0 equation: 


Simplifying
(4x3y + -4y3) * dy + -1(6x5 + 6x2y2) * dx = 0

Reorder the terms for easier multiplication:
dy(4x3y + -4y3) + -1(6x5 + 6x2y2) * dx = 0
(4x3y * dy + -4y3 * dy) + -1(6x5 + 6x2y2) * dx = 0
(4dx3y2 + -4dy4) + -1(6x5 + 6x2y2) * dx = 0

Reorder the terms:
4dx3y2 + -4dy4 + -1(6x2y2 + 6x5) * dx = 0

Reorder the terms for easier multiplication:
4dx3y2 + -4dy4 + -1dx(6x2y2 + 6x5) = 0
4dx3y2 + -4dy4 + (6x2y2 * -1dx + 6x5 * -1dx) = 0
4dx3y2 + -4dy4 + (-6dx3y2 + -6dx6) = 0

Reorder the terms:
4dx3y2 + -6dx3y2 + -6dx6 + -4dy4 = 0

Combine like terms: 4dx3y2 + -6dx3y2 = -2dx3y2
-2dx3y2 + -6dx6 + -4dy4 = 0

Solving
-2dx3y2 + -6dx6 + -4dy4 = 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), '-2d'.
-2d(x3y2 + 3x6 + 2y4) = 0

Ignore the factor -2.

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 '(x3y2 + 3x6 + 2y4)' equal to zero and attempt to solve:

Simplifying
x3y2 + 3x6 + 2y4 = 0

Solving
x3y2 + 3x6 + 2y4 = 0

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

Add '-1x3y2' to each side of the equation.
x3y2 + 3x6 + -1x3y2 + 2y4 = 0 + -1x3y2

Reorder the terms:
x3y2 + -1x3y2 + 3x6 + 2y4 = 0 + -1x3y2

Combine like terms: x3y2 + -1x3y2 = 0
0 + 3x6 + 2y4 = 0 + -1x3y2
3x6 + 2y4 = 0 + -1x3y2
Remove the zero:
3x6 + 2y4 = -1x3y2

Add '-3x6' to each side of the equation.
3x6 + -3x6 + 2y4 = -1x3y2 + -3x6

Combine like terms: 3x6 + -3x6 = 0
0 + 2y4 = -1x3y2 + -3x6
2y4 = -1x3y2 + -3x6

Add '-2y4' to each side of the equation.
2y4 + -2y4 = -1x3y2 + -3x6 + -2y4

Combine like terms: 2y4 + -2y4 = 0
0 = -1x3y2 + -3x6 + -2y4

Simplifying
0 = -1x3y2 + -3x6 + -2y4

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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