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

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


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

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

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

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

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

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

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

Solving
3dx + -2dy = 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 + -2y) = 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 + -2y)' equal to zero and attempt to solve:

Simplifying
3x + -2y = 0

Solving
3x + -2y = 0

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

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

Combine like terms: 3x + -3x = 0
0 + -2y = 0 + -3x
-2y = 0 + -3x
Remove the zero:
-2y = -3x

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

Combine like terms: -2y + 2y = 0
0 = -3x + 2y

Simplifying
0 = -3x + 2y

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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