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

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

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

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

Reorder the terms:
(-3dxy + 2dx2) + -3(x + -2y2) * dy = 0
(-3dxy + 2dx2) + -3(x + -2y2) * dy = 0

Reorder the terms for easier multiplication:
-3dxy + 2dx2 + -3dy(x + -2y2) = 0
-3dxy + 2dx2 + (x * -3dy + -2y2 * -3dy) = 0
-3dxy + 2dx2 + (-3dxy + 6dy3) = 0

Reorder the terms:
-3dxy + -3dxy + 2dx2 + 6dy3 = 0

Combine like terms: -3dxy + -3dxy = -6dxy
-6dxy + 2dx2 + 6dy3 = 0

Solving
-6dxy + 2dx2 + 6dy3 = 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(-3xy + x2 + 3y3) = 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 '(-3xy + x2 + 3y3)' equal to zero and attempt to solve:

Simplifying
-3xy + x2 + 3y3 = 0

Solving
-3xy + x2 + 3y3 = 0

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

Add '3xy' to each side of the equation.
-3xy + x2 + 3xy + 3y3 = 0 + 3xy

Reorder the terms:
-3xy + 3xy + x2 + 3y3 = 0 + 3xy

Combine like terms: -3xy + 3xy = 0
0 + x2 + 3y3 = 0 + 3xy
x2 + 3y3 = 0 + 3xy
Remove the zero:
x2 + 3y3 = 3xy

Add '-1x2' to each side of the equation.
x2 + -1x2 + 3y3 = 3xy + -1x2

Combine like terms: x2 + -1x2 = 0
0 + 3y3 = 3xy + -1x2
3y3 = 3xy + -1x2

Add '-3y3' to each side of the equation.
3y3 + -3y3 = 3xy + -1x2 + -3y3

Combine like terms: 3y3 + -3y3 = 0
0 = 3xy + -1x2 + -3y3

Simplifying
0 = 3xy + -1x2 + -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}