(y+4)dx+(x-5)dy=0

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Solution for (y+4)dx+(x-5)dy=0 equation: 


Simplifying
(y + 4) * dx + (x + -5) * dy = 0

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

Reorder the terms for easier multiplication:
dx(4 + y) + (x + -5) * dy = 0
(4 * dx + y * dx) + (x + -5) * dy = 0
(4dx + dxy) + (x + -5) * dy = 0

Reorder the terms:
4dx + dxy + (-5 + x) * dy = 0

Reorder the terms for easier multiplication:
4dx + dxy + dy(-5 + x) = 0
4dx + dxy + (-5 * dy + x * dy) = 0

Reorder the terms:
4dx + dxy + (dxy + -5dy) = 0
4dx + dxy + (dxy + -5dy) = 0

Combine like terms: dxy + dxy = 2dxy
4dx + 2dxy + -5dy = 0

Solving
4dx + 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(4x + 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 '(4x + 2xy + -5y)' equal to zero and attempt to solve:

Simplifying
4x + 2xy + -5y = 0

Solving
4x + 2xy + -5y = 0

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

Add '-4x' to each side of the equation.
4x + 2xy + -4x + -5y = 0 + -4x

Reorder the terms:
4x + -4x + 2xy + -5y = 0 + -4x

Combine like terms: 4x + -4x = 0
0 + 2xy + -5y = 0 + -4x
2xy + -5y = 0 + -4x
Remove the zero:
2xy + -5y = -4x

Add '-2xy' to each side of the equation.
2xy + -2xy + -5y = -4x + -2xy

Combine like terms: 2xy + -2xy = 0
0 + -5y = -4x + -2xy
-5y = -4x + -2xy

Add '5y' to each side of the equation.
-5y + 5y = -4x + -2xy + 5y

Combine like terms: -5y + 5y = 0
0 = -4x + -2xy + 5y

Simplifying
0 = -4x + -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}

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