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

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


Simplifying
(3x2 + 2xy2 + -2x) * dx + (3y2 + 2x2y + -2y) * dy = 0

Reorder the terms:
(-2x + 2xy2 + 3x2) * dx + (3y2 + 2x2y + -2y) * dy = 0

Reorder the terms for easier multiplication:
dx(-2x + 2xy2 + 3x2) + (3y2 + 2x2y + -2y) * dy = 0
(-2x * dx + 2xy2 * dx + 3x2 * dx) + (3y2 + 2x2y + -2y) * dy = 0
(-2dx2 + 2dx2y2 + 3dx3) + (3y2 + 2x2y + -2y) * dy = 0

Reorder the terms:
-2dx2 + 2dx2y2 + 3dx3 + (2x2y + -2y + 3y2) * dy = 0

Reorder the terms for easier multiplication:
-2dx2 + 2dx2y2 + 3dx3 + dy(2x2y + -2y + 3y2) = 0
-2dx2 + 2dx2y2 + 3dx3 + (2x2y * dy + -2y * dy + 3y2 * dy) = 0
-2dx2 + 2dx2y2 + 3dx3 + (2dx2y2 + -2dy2 + 3dy3) = 0

Reorder the terms:
-2dx2 + 2dx2y2 + 2dx2y2 + 3dx3 + -2dy2 + 3dy3 = 0

Combine like terms: 2dx2y2 + 2dx2y2 = 4dx2y2
-2dx2 + 4dx2y2 + 3dx3 + -2dy2 + 3dy3 = 0

Solving
-2dx2 + 4dx2y2 + 3dx3 + -2dy2 + 3dy3 = 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(-2x2 + 4x2y2 + 3x3 + -2y2 + 3y3) = 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 '(-2x2 + 4x2y2 + 3x3 + -2y2 + 3y3)' equal to zero and attempt to solve:

Simplifying
-2x2 + 4x2y2 + 3x3 + -2y2 + 3y3 = 0

Solving
-2x2 + 4x2y2 + 3x3 + -2y2 + 3y3 = 0

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

Add '2x2' to each side of the equation.
-2x2 + 4x2y2 + 3x3 + -2y2 + 2x2 + 3y3 = 0 + 2x2

Reorder the terms:
-2x2 + 2x2 + 4x2y2 + 3x3 + -2y2 + 3y3 = 0 + 2x2

Combine like terms: -2x2 + 2x2 = 0
0 + 4x2y2 + 3x3 + -2y2 + 3y3 = 0 + 2x2
4x2y2 + 3x3 + -2y2 + 3y3 = 0 + 2x2
Remove the zero:
4x2y2 + 3x3 + -2y2 + 3y3 = 2x2

Add '-4x2y2' to each side of the equation.
4x2y2 + 3x3 + -2y2 + -4x2y2 + 3y3 = 2x2 + -4x2y2

Reorder the terms:
4x2y2 + -4x2y2 + 3x3 + -2y2 + 3y3 = 2x2 + -4x2y2

Combine like terms: 4x2y2 + -4x2y2 = 0
0 + 3x3 + -2y2 + 3y3 = 2x2 + -4x2y2
3x3 + -2y2 + 3y3 = 2x2 + -4x2y2

Add '-3x3' to each side of the equation.
3x3 + -2y2 + -3x3 + 3y3 = 2x2 + -4x2y2 + -3x3

Reorder the terms:
3x3 + -3x3 + -2y2 + 3y3 = 2x2 + -4x2y2 + -3x3

Combine like terms: 3x3 + -3x3 = 0
0 + -2y2 + 3y3 = 2x2 + -4x2y2 + -3x3
-2y2 + 3y3 = 2x2 + -4x2y2 + -3x3

Add '2y2' to each side of the equation.
-2y2 + 2y2 + 3y3 = 2x2 + -4x2y2 + -3x3 + 2y2

Combine like terms: -2y2 + 2y2 = 0
0 + 3y3 = 2x2 + -4x2y2 + -3x3 + 2y2
3y3 = 2x2 + -4x2y2 + -3x3 + 2y2

Add '-3y3' to each side of the equation.
3y3 + -3y3 = 2x2 + -4x2y2 + -3x3 + 2y2 + -3y3

Combine like terms: 3y3 + -3y3 = 0
0 = 2x2 + -4x2y2 + -3x3 + 2y2 + -3y3

Simplifying
0 = 2x2 + -4x2y2 + -3x3 + 2y2 + -3y3

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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