(5x-3y)dx+(8x-3y)dy=0

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Solution for (5x-3y)dx+(8x-3y)dy=0 equation: 


Simplifying
(5x + -3y) * dx + (8x + -3y) * dy = 0

Reorder the terms for easier multiplication:
dx(5x + -3y) + (8x + -3y) * dy = 0
(5x * dx + -3y * dx) + (8x + -3y) * dy = 0

Reorder the terms:
(-3dxy + 5dx2) + (8x + -3y) * dy = 0
(-3dxy + 5dx2) + (8x + -3y) * dy = 0

Reorder the terms for easier multiplication:
-3dxy + 5dx2 + dy(8x + -3y) = 0
-3dxy + 5dx2 + (8x * dy + -3y * dy) = 0
-3dxy + 5dx2 + (8dxy + -3dy2) = 0

Reorder the terms:
-3dxy + 8dxy + 5dx2 + -3dy2 = 0

Combine like terms: -3dxy + 8dxy = 5dxy
5dxy + 5dx2 + -3dy2 = 0

Solving
5dxy + 5dx2 + -3dy2 = 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(5xy + 5x2 + -3y2) = 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 '(5xy + 5x2 + -3y2)' equal to zero and attempt to solve:

Simplifying
5xy + 5x2 + -3y2 = 0

Solving
5xy + 5x2 + -3y2 = 0

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

Add '-5xy' to each side of the equation.
5xy + 5x2 + -5xy + -3y2 = 0 + -5xy

Reorder the terms:
5xy + -5xy + 5x2 + -3y2 = 0 + -5xy

Combine like terms: 5xy + -5xy = 0
0 + 5x2 + -3y2 = 0 + -5xy
5x2 + -3y2 = 0 + -5xy
Remove the zero:
5x2 + -3y2 = -5xy

Add '-5x2' to each side of the equation.
5x2 + -5x2 + -3y2 = -5xy + -5x2

Combine like terms: 5x2 + -5x2 = 0
0 + -3y2 = -5xy + -5x2
-3y2 = -5xy + -5x2

Add '3y2' to each side of the equation.
-3y2 + 3y2 = -5xy + -5x2 + 3y2

Combine like terms: -3y2 + 3y2 = 0
0 = -5xy + -5x2 + 3y2

Simplifying
0 = -5xy + -5x2 + 3y2

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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