(x+1)dy-(y+8)dx=0

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Solution for (x+1)dy-(y+8)dx=0 equation: 


Simplifying
(x + 1) * dy + -1(y + 8) * dx = 0

Reorder the terms:
(1 + x) * dy + -1(y + 8) * dx = 0

Reorder the terms for easier multiplication:
dy(1 + x) + -1(y + 8) * dx = 0
(1 * dy + x * dy) + -1(y + 8) * dx = 0

Reorder the terms:
(dxy + 1dy) + -1(y + 8) * dx = 0
(dxy + 1dy) + -1(y + 8) * dx = 0

Reorder the terms:
dxy + 1dy + -1(8 + y) * dx = 0

Reorder the terms for easier multiplication:
dxy + 1dy + -1dx(8 + y) = 0
dxy + 1dy + (8 * -1dx + y * -1dx) = 0
dxy + 1dy + (-8dx + -1dxy) = 0

Reorder the terms:
-8dx + dxy + -1dxy + 1dy = 0

Combine like terms: dxy + -1dxy = 0
-8dx + 0 + 1dy = 0
-8dx + 1dy = 0

Solving
-8dx + 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(-8x + y) = 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 '(-8x + y)' equal to zero and attempt to solve:

Simplifying
-8x + y = 0

Solving
-8x + y = 0

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

Add '8x' to each side of the equation.
-8x + 8x + y = 0 + 8x

Combine like terms: -8x + 8x = 0
0 + y = 0 + 8x
y = 0 + 8x
Remove the zero:
y = 8x

Add '-1y' to each side of the equation.
y + -1y = 8x + -1y

Combine like terms: y + -1y = 0
0 = 8x + -1y

Simplifying
0 = 8x + -1y

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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