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

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


Simplifying
(6x2y2 + 2xy3 + 3) * dx + (3x2y2 + 6x3y + -2) * dy = 0

Reorder the terms:
(3 + 2xy3 + 6x2y2) * dx + (3x2y2 + 6x3y + -2) * dy = 0

Reorder the terms for easier multiplication:
dx(3 + 2xy3 + 6x2y2) + (3x2y2 + 6x3y + -2) * dy = 0
(3 * dx + 2xy3 * dx + 6x2y2 * dx) + (3x2y2 + 6x3y + -2) * dy = 0
(3dx + 2dx2y3 + 6dx3y2) + (3x2y2 + 6x3y + -2) * dy = 0

Reorder the terms:
3dx + 2dx2y3 + 6dx3y2 + (-2 + 3x2y2 + 6x3y) * dy = 0

Reorder the terms for easier multiplication:
3dx + 2dx2y3 + 6dx3y2 + dy(-2 + 3x2y2 + 6x3y) = 0
3dx + 2dx2y3 + 6dx3y2 + (-2 * dy + 3x2y2 * dy + 6x3y * dy) = 0

Reorder the terms:
3dx + 2dx2y3 + 6dx3y2 + (3dx2y3 + 6dx3y2 + -2dy) = 0
3dx + 2dx2y3 + 6dx3y2 + (3dx2y3 + 6dx3y2 + -2dy) = 0

Reorder the terms:
3dx + 2dx2y3 + 3dx2y3 + 6dx3y2 + 6dx3y2 + -2dy = 0

Combine like terms: 2dx2y3 + 3dx2y3 = 5dx2y3
3dx + 5dx2y3 + 6dx3y2 + 6dx3y2 + -2dy = 0

Combine like terms: 6dx3y2 + 6dx3y2 = 12dx3y2
3dx + 5dx2y3 + 12dx3y2 + -2dy = 0

Solving
3dx + 5dx2y3 + 12dx3y2 + -2dy = 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(3x + 5x2y3 + 12x3y2 + -2y) = 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 '(3x + 5x2y3 + 12x3y2 + -2y)' equal to zero and attempt to solve:

Simplifying
3x + 5x2y3 + 12x3y2 + -2y = 0

Solving
3x + 5x2y3 + 12x3y2 + -2y = 0

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

Add '-3x' to each side of the equation.
3x + 5x2y3 + 12x3y2 + -3x + -2y = 0 + -3x

Reorder the terms:
3x + -3x + 5x2y3 + 12x3y2 + -2y = 0 + -3x

Combine like terms: 3x + -3x = 0
0 + 5x2y3 + 12x3y2 + -2y = 0 + -3x
5x2y3 + 12x3y2 + -2y = 0 + -3x
Remove the zero:
5x2y3 + 12x3y2 + -2y = -3x

Add '-5x2y3' to each side of the equation.
5x2y3 + 12x3y2 + -5x2y3 + -2y = -3x + -5x2y3

Reorder the terms:
5x2y3 + -5x2y3 + 12x3y2 + -2y = -3x + -5x2y3

Combine like terms: 5x2y3 + -5x2y3 = 0
0 + 12x3y2 + -2y = -3x + -5x2y3
12x3y2 + -2y = -3x + -5x2y3

Add '-12x3y2' to each side of the equation.
12x3y2 + -12x3y2 + -2y = -3x + -5x2y3 + -12x3y2

Combine like terms: 12x3y2 + -12x3y2 = 0
0 + -2y = -3x + -5x2y3 + -12x3y2
-2y = -3x + -5x2y3 + -12x3y2

Add '2y' to each side of the equation.
-2y + 2y = -3x + -5x2y3 + -12x3y2 + 2y

Combine like terms: -2y + 2y = 0
0 = -3x + -5x2y3 + -12x3y2 + 2y

Simplifying
0 = -3x + -5x2y3 + -12x3y2 + 2y

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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