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

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


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

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

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

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

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

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

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

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

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

Simplifying
-2x + 2xy + -1y = 0

Solving
-2x + 2xy + -1y = 0

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

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

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

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

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

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

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

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

Simplifying
0 = 2x + -2xy + y

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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