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

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


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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Simplifying
0 = -2xy + -1x2 + 4y + 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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