(x-y+3)dy-(2x+3y-4)dx=0

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Solution for (x-y+3)dy-(2x+3y-4)dx=0 equation: 


Simplifying
(x + -1y + 3) * dy + -1(2x + 3y + -4) * dx = 0

Reorder the terms:
(3 + x + -1y) * dy + -1(2x + 3y + -4) * dx = 0

Reorder the terms for easier multiplication:
dy(3 + x + -1y) + -1(2x + 3y + -4) * dx = 0
(3 * dy + x * dy + -1y * dy) + -1(2x + 3y + -4) * dx = 0

Reorder the terms:
(dxy + 3dy + -1dy2) + -1(2x + 3y + -4) * dx = 0
(dxy + 3dy + -1dy2) + -1(2x + 3y + -4) * dx = 0

Reorder the terms:
dxy + 3dy + -1dy2 + -1(-4 + 2x + 3y) * dx = 0

Reorder the terms for easier multiplication:
dxy + 3dy + -1dy2 + -1dx(-4 + 2x + 3y) = 0
dxy + 3dy + -1dy2 + (-4 * -1dx + 2x * -1dx + 3y * -1dx) = 0

Reorder the terms:
dxy + 3dy + -1dy2 + (4dx + -3dxy + -2dx2) = 0
dxy + 3dy + -1dy2 + (4dx + -3dxy + -2dx2) = 0

Reorder the terms:
4dx + dxy + -3dxy + -2dx2 + 3dy + -1dy2 = 0

Combine like terms: dxy + -3dxy = -2dxy
4dx + -2dxy + -2dx2 + 3dy + -1dy2 = 0

Solving
4dx + -2dxy + -2dx2 + 3dy + -1dy2 = 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(4x + -2xy + -2x2 + 3y + -1y2) = 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 '(4x + -2xy + -2x2 + 3y + -1y2)' equal to zero and attempt to solve:

Simplifying
4x + -2xy + -2x2 + 3y + -1y2 = 0

Solving
4x + -2xy + -2x2 + 3y + -1y2 = 0

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

Add '-4x' to each side of the equation.
4x + -2xy + -2x2 + 3y + -4x + -1y2 = 0 + -4x

Reorder the terms:
4x + -4x + -2xy + -2x2 + 3y + -1y2 = 0 + -4x

Combine like terms: 4x + -4x = 0
0 + -2xy + -2x2 + 3y + -1y2 = 0 + -4x
-2xy + -2x2 + 3y + -1y2 = 0 + -4x
Remove the zero:
-2xy + -2x2 + 3y + -1y2 = -4x

Add '2xy' to each side of the equation.
-2xy + -2x2 + 3y + 2xy + -1y2 = -4x + 2xy

Reorder the terms:
-2xy + 2xy + -2x2 + 3y + -1y2 = -4x + 2xy

Combine like terms: -2xy + 2xy = 0
0 + -2x2 + 3y + -1y2 = -4x + 2xy
-2x2 + 3y + -1y2 = -4x + 2xy

Add '2x2' to each side of the equation.
-2x2 + 3y + 2x2 + -1y2 = -4x + 2xy + 2x2

Reorder the terms:
-2x2 + 2x2 + 3y + -1y2 = -4x + 2xy + 2x2

Combine like terms: -2x2 + 2x2 = 0
0 + 3y + -1y2 = -4x + 2xy + 2x2
3y + -1y2 = -4x + 2xy + 2x2

Add '-3y' to each side of the equation.
3y + -3y + -1y2 = -4x + 2xy + 2x2 + -3y

Combine like terms: 3y + -3y = 0
0 + -1y2 = -4x + 2xy + 2x2 + -3y
-1y2 = -4x + 2xy + 2x2 + -3y

Add 'y2' to each side of the equation.
-1y2 + y2 = -4x + 2xy + 2x2 + -3y + y2

Combine like terms: -1y2 + y2 = 0
0 = -4x + 2xy + 2x2 + -3y + y2

Simplifying
0 = -4x + 2xy + 2x2 + -3y + y2

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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