(x+5)dy+(y-5)dx=0

Solution for (x+5)dy+(y-5)dx=0 equation:

Simplifying
(x + 5) * dy + (y + -5) * dx = 0

Reorder the terms:
(5 + x) * dy + (y + -5) * dx = 0

Reorder the terms for easier multiplication:
dy(5 + x) + (y + -5) * dx = 0
(5 * dy + x * dy) + (y + -5) * dx = 0

Reorder the terms:
(dxy + 5dy) + (y + -5) * dx = 0
(dxy + 5dy) + (y + -5) * dx = 0

Reorder the terms:
dxy + 5dy + (-5 + y) * dx = 0

Reorder the terms for easier multiplication:
dxy + 5dy + dx(-5 + y) = 0
dxy + 5dy + (-5 * dx + y * dx) = 0
dxy + 5dy + (-5dx + dxy) = 0

Reorder the terms:
-5dx + dxy + dxy + 5dy = 0

Combine like terms: dxy + dxy = 2dxy
-5dx + 2dxy + 5dy = 0

Solving
-5dx + 2dxy + 5dy = 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(-5x + 2xy + 5y) = 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 '(-5x + 2xy + 5y)' equal to zero and attempt to solve:

Simplifying
-5x + 2xy + 5y = 0

Solving
-5x + 2xy + 5y = 0

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

Add '5x' to each side of the equation.
-5x + 2xy + 5x + 5y = 0 + 5x

Reorder the terms:
-5x + 5x + 2xy + 5y = 0 + 5x

Combine like terms: -5x + 5x = 0
0 + 2xy + 5y = 0 + 5x
2xy + 5y = 0 + 5x
Remove the zero:
2xy + 5y = 5x

Add '-2xy' to each side of the equation.
2xy + -2xy + 5y = 5x + -2xy

Combine like terms: 2xy + -2xy = 0
0 + 5y = 5x + -2xy
5y = 5x + -2xy

Add '-5y' to each side of the equation.
5y + -5y = 5x + -2xy + -5y

Combine like terms: 5y + -5y = 0
0 = 5x + -2xy + -5y

Simplifying
0 = 5x + -2xy + -5y

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
d = {0}