(5y-2x)*dy+(3x+2y)dx=0

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Solution for (5y-2x)*dy+(3x+2y)dx=0 equation: 


Simplifying
(5y + -2x) * dy + (3x + 2y) * dx = 0

Reorder the terms:
(-2x + 5y) * dy + (3x + 2y) * dx = 0

Reorder the terms for easier multiplication:
dy(-2x + 5y) + (3x + 2y) * dx = 0
(-2x * dy + 5y * dy) + (3x + 2y) * dx = 0
(-2dxy + 5dy2) + (3x + 2y) * dx = 0

Reorder the terms for easier multiplication:
-2dxy + 5dy2 + dx(3x + 2y) = 0
-2dxy + 5dy2 + (3x * dx + 2y * dx) = 0

Reorder the terms:
-2dxy + 5dy2 + (2dxy + 3dx2) = 0
-2dxy + 5dy2 + (2dxy + 3dx2) = 0

Reorder the terms:
-2dxy + 2dxy + 3dx2 + 5dy2 = 0

Combine like terms: -2dxy + 2dxy = 0
0 + 3dx2 + 5dy2 = 0
3dx2 + 5dy2 = 0

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

Simplifying
3x2 + 5y2 = 0

Solving
3x2 + 5y2 = 0

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

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

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

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

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

Simplifying
0 = -3x2 + -5y2

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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