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

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


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

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

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

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

Combine like terms: 2dxy + 2dxy = 4dxy
-3dx + 4dxy + 3dy3 = 0

Solving
-3dx + 4dxy + 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 + 4xy + 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 + 4xy + 3y3)' equal to zero and attempt to solve:

Simplifying
-3x + 4xy + 3y3 = 0

Solving
-3x + 4xy + 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 + 4xy + 3x + 3y3 = 0 + 3x

Reorder the terms:
-3x + 3x + 4xy + 3y3 = 0 + 3x

Combine like terms: -3x + 3x = 0
0 + 4xy + 3y3 = 0 + 3x
4xy + 3y3 = 0 + 3x
Remove the zero:
4xy + 3y3 = 3x

Add '-4xy' to each side of the equation.
4xy + -4xy + 3y3 = 3x + -4xy

Combine like terms: 4xy + -4xy = 0
0 + 3y3 = 3x + -4xy
3y3 = 3x + -4xy

Add '-3y3' to each side of the equation.
3y3 + -3y3 = 3x + -4xy + -3y3

Combine like terms: 3y3 + -3y3 = 0
0 = 3x + -4xy + -3y3

Simplifying
0 = 3x + -4xy + -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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