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

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


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

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

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

Reorder the terms:
(3dx + -2dxy + 3dx3y) + (x2 + 2x + 3y2) * dy = 0
(3dx + -2dxy + 3dx3y) + (x2 + 2x + 3y2) * dy = 0

Reorder the terms:
3dx + -2dxy + 3dx3y + (2x + x2 + 3y2) * dy = 0

Reorder the terms for easier multiplication:
3dx + -2dxy + 3dx3y + dy(2x + x2 + 3y2) = 0
3dx + -2dxy + 3dx3y + (2x * dy + x2 * dy + 3y2 * dy) = 0
3dx + -2dxy + 3dx3y + (2dxy + dx2y + 3dy3) = 0

Reorder the terms:
3dx + -2dxy + 2dxy + dx2y + 3dx3y + 3dy3 = 0

Combine like terms: -2dxy + 2dxy = 0
3dx + 0 + dx2y + 3dx3y + 3dy3 = 0
3dx + dx2y + 3dx3y + 3dy3 = 0

Solving
3dx + dx2y + 3dx3y + 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(3x + x2y + 3x3y + 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 '(3x + x2y + 3x3y + 3y3)' equal to zero and attempt to solve:

Simplifying
3x + x2y + 3x3y + 3y3 = 0

Solving
3x + x2y + 3x3y + 3y3 = 0

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

Add '-3x' to each side of the equation.
3x + x2y + 3x3y + -3x + 3y3 = 0 + -3x

Reorder the terms:
3x + -3x + x2y + 3x3y + 3y3 = 0 + -3x

Combine like terms: 3x + -3x = 0
0 + x2y + 3x3y + 3y3 = 0 + -3x
x2y + 3x3y + 3y3 = 0 + -3x
Remove the zero:
x2y + 3x3y + 3y3 = -3x

Add '-1x2y' to each side of the equation.
x2y + 3x3y + -1x2y + 3y3 = -3x + -1x2y

Reorder the terms:
x2y + -1x2y + 3x3y + 3y3 = -3x + -1x2y

Combine like terms: x2y + -1x2y = 0
0 + 3x3y + 3y3 = -3x + -1x2y
3x3y + 3y3 = -3x + -1x2y

Add '-3x3y' to each side of the equation.
3x3y + -3x3y + 3y3 = -3x + -1x2y + -3x3y

Combine like terms: 3x3y + -3x3y = 0
0 + 3y3 = -3x + -1x2y + -3x3y
3y3 = -3x + -1x2y + -3x3y

Add '-3y3' to each side of the equation.
3y3 + -3y3 = -3x + -1x2y + -3x3y + -3y3

Combine like terms: 3y3 + -3y3 = 0
0 = -3x + -1x2y + -3x3y + -3y3

Simplifying
0 = -3x + -1x2y + -3x3y + -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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