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

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


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

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

Reorder the terms for easier multiplication:
dy(4 + y) + (x + -5) * dx = 0
(4 * dy + y * dy) + (x + -5) * dx = 0
(4dy + dy2) + (x + -5) * dx = 0

Reorder the terms:
4dy + dy2 + (-5 + x) * dx = 0

Reorder the terms for easier multiplication:
4dy + dy2 + dx(-5 + x) = 0
4dy + dy2 + (-5 * dx + x * dx) = 0
4dy + dy2 + (-5dx + dx2) = 0

Reorder the terms:
-5dx + dx2 + 4dy + dy2 = 0

Solving
-5dx + dx2 + 4dy + dy2 = 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 + x2 + 4y + y2) = 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 + x2 + 4y + y2)' equal to zero and attempt to solve:

Simplifying
-5x + x2 + 4y + y2 = 0

Solving
-5x + x2 + 4y + y2 = 0

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

Add '5x' to each side of the equation.
-5x + x2 + 4y + 5x + y2 = 0 + 5x

Reorder the terms:
-5x + 5x + x2 + 4y + y2 = 0 + 5x

Combine like terms: -5x + 5x = 0
0 + x2 + 4y + y2 = 0 + 5x
x2 + 4y + y2 = 0 + 5x
Remove the zero:
x2 + 4y + y2 = 5x

Add '-1x2' to each side of the equation.
x2 + 4y + -1x2 + y2 = 5x + -1x2

Reorder the terms:
x2 + -1x2 + 4y + y2 = 5x + -1x2

Combine like terms: x2 + -1x2 = 0
0 + 4y + y2 = 5x + -1x2
4y + y2 = 5x + -1x2

Add '-4y' to each side of the equation.
4y + -4y + y2 = 5x + -1x2 + -4y

Combine like terms: 4y + -4y = 0
0 + y2 = 5x + -1x2 + -4y
y2 = 5x + -1x2 + -4y

Add '-1y2' to each side of the equation.
y2 + -1y2 = 5x + -1x2 + -4y + -1y2

Combine like terms: y2 + -1y2 = 0
0 = 5x + -1x2 + -4y + -1y2

Simplifying
0 = 5x + -1x2 + -4y + -1y2

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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