(3x-2y+3)dy-(2y-3x-1)dx=0

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Solution for (3x-2y+3)dy-(2y-3x-1)dx=0 equation: 


Simplifying
(3x + -2y + 3) * dy + -1(2y + -3x + -1) * dx = 0

Reorder the terms:
(3 + 3x + -2y) * dy + -1(2y + -3x + -1) * dx = 0

Reorder the terms for easier multiplication:
dy(3 + 3x + -2y) + -1(2y + -3x + -1) * dx = 0
(3 * dy + 3x * dy + -2y * dy) + -1(2y + -3x + -1) * dx = 0

Reorder the terms:
(3dxy + 3dy + -2dy2) + -1(2y + -3x + -1) * dx = 0
(3dxy + 3dy + -2dy2) + -1(2y + -3x + -1) * dx = 0

Reorder the terms:
3dxy + 3dy + -2dy2 + -1(-1 + -3x + 2y) * dx = 0

Reorder the terms for easier multiplication:
3dxy + 3dy + -2dy2 + -1dx(-1 + -3x + 2y) = 0
3dxy + 3dy + -2dy2 + (-1 * -1dx + -3x * -1dx + 2y * -1dx) = 0

Reorder the terms:
3dxy + 3dy + -2dy2 + (1dx + -2dxy + 3dx2) = 0
3dxy + 3dy + -2dy2 + (1dx + -2dxy + 3dx2) = 0

Reorder the terms:
1dx + 3dxy + -2dxy + 3dx2 + 3dy + -2dy2 = 0

Combine like terms: 3dxy + -2dxy = 1dxy
1dx + 1dxy + 3dx2 + 3dy + -2dy2 = 0

Solving
1dx + 1dxy + 3dx2 + 3dy + -2dy2 = 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(x + xy + 3x2 + 3y + -2y2) = 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 '(x + xy + 3x2 + 3y + -2y2)' equal to zero and attempt to solve:

Simplifying
x + xy + 3x2 + 3y + -2y2 = 0

Solving
x + xy + 3x2 + 3y + -2y2 = 0

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

Add '-1x' to each side of the equation.
x + xy + 3x2 + 3y + -1x + -2y2 = 0 + -1x

Reorder the terms:
x + -1x + xy + 3x2 + 3y + -2y2 = 0 + -1x

Combine like terms: x + -1x = 0
0 + xy + 3x2 + 3y + -2y2 = 0 + -1x
xy + 3x2 + 3y + -2y2 = 0 + -1x
Remove the zero:
xy + 3x2 + 3y + -2y2 = -1x

Add '-1xy' to each side of the equation.
xy + 3x2 + 3y + -1xy + -2y2 = -1x + -1xy

Reorder the terms:
xy + -1xy + 3x2 + 3y + -2y2 = -1x + -1xy

Combine like terms: xy + -1xy = 0
0 + 3x2 + 3y + -2y2 = -1x + -1xy
3x2 + 3y + -2y2 = -1x + -1xy

Add '-3x2' to each side of the equation.
3x2 + 3y + -3x2 + -2y2 = -1x + -1xy + -3x2

Reorder the terms:
3x2 + -3x2 + 3y + -2y2 = -1x + -1xy + -3x2

Combine like terms: 3x2 + -3x2 = 0
0 + 3y + -2y2 = -1x + -1xy + -3x2
3y + -2y2 = -1x + -1xy + -3x2

Add '-3y' to each side of the equation.
3y + -3y + -2y2 = -1x + -1xy + -3x2 + -3y

Combine like terms: 3y + -3y = 0
0 + -2y2 = -1x + -1xy + -3x2 + -3y
-2y2 = -1x + -1xy + -3x2 + -3y

Add '2y2' to each side of the equation.
-2y2 + 2y2 = -1x + -1xy + -3x2 + -3y + 2y2

Combine like terms: -2y2 + 2y2 = 0
0 = -1x + -1xy + -3x2 + -3y + 2y2

Simplifying
0 = -1x + -1xy + -3x2 + -3y + 2y2

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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