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

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


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

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

Reorder the terms:
(2dxy + 3dx3) + (2x + -3) * dy = 0
(2dxy + 3dx3) + (2x + -3) * dy = 0

Reorder the terms:
2dxy + 3dx3 + (-3 + 2x) * dy = 0

Reorder the terms for easier multiplication:
2dxy + 3dx3 + dy(-3 + 2x) = 0
2dxy + 3dx3 + (-3 * dy + 2x * dy) = 0

Reorder the terms:
2dxy + 3dx3 + (2dxy + -3dy) = 0
2dxy + 3dx3 + (2dxy + -3dy) = 0

Reorder the terms:
2dxy + 2dxy + 3dx3 + -3dy = 0

Combine like terms: 2dxy + 2dxy = 4dxy
4dxy + 3dx3 + -3dy = 0

Solving
4dxy + 3dx3 + -3dy = 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(4xy + 3x3 + -3y) = 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 '(4xy + 3x3 + -3y)' equal to zero and attempt to solve:

Simplifying
4xy + 3x3 + -3y = 0

Solving
4xy + 3x3 + -3y = 0

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

Add '-4xy' to each side of the equation.
4xy + 3x3 + -4xy + -3y = 0 + -4xy

Reorder the terms:
4xy + -4xy + 3x3 + -3y = 0 + -4xy

Combine like terms: 4xy + -4xy = 0
0 + 3x3 + -3y = 0 + -4xy
3x3 + -3y = 0 + -4xy
Remove the zero:
3x3 + -3y = -4xy

Add '-3x3' to each side of the equation.
3x3 + -3x3 + -3y = -4xy + -3x3

Combine like terms: 3x3 + -3x3 = 0
0 + -3y = -4xy + -3x3
-3y = -4xy + -3x3

Add '3y' to each side of the equation.
-3y + 3y = -4xy + -3x3 + 3y

Combine like terms: -3y + 3y = 0
0 = -4xy + -3x3 + 3y

Simplifying
0 = -4xy + -3x3 + 3y

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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