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

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


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

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

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

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

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

Reorder the terms for easier multiplication:
4dx + 3dxy + -2dx2 + -1dy(-2 + 4x + -3y) = 0
4dx + 3dxy + -2dx2 + (-2 * -1dy + 4x * -1dy + -3y * -1dy) = 0

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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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