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

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


Simplifying
(3y + -5x) * dy + -1(5y + -3x) * dx = 0

Reorder the terms:
(-5x + 3y) * dy + -1(5y + -3x) * dx = 0

Reorder the terms for easier multiplication:
dy(-5x + 3y) + -1(5y + -3x) * dx = 0
(-5x * dy + 3y * dy) + -1(5y + -3x) * dx = 0
(-5dxy + 3dy2) + -1(5y + -3x) * dx = 0

Reorder the terms:
-5dxy + 3dy2 + -1(-3x + 5y) * dx = 0

Reorder the terms for easier multiplication:
-5dxy + 3dy2 + -1dx(-3x + 5y) = 0
-5dxy + 3dy2 + (-3x * -1dx + 5y * -1dx) = 0

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

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

Combine like terms: -5dxy + -5dxy = -10dxy
-10dxy + 3dx2 + 3dy2 = 0

Solving
-10dxy + 3dx2 + 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(-10xy + 3x2 + 3y2) = 0

Factor a trinomial.
d((x + -3y)(3x + -1y)) = 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 '(x + -3y)' equal to zero and attempt to solve:

Simplifying
x + -3y = 0

Solving
x + -3y = 0

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

Add '-1x' to each side of the equation.
x + -1x + -3y = 0 + -1x

Combine like terms: x + -1x = 0
0 + -3y = 0 + -1x
-3y = 0 + -1x
Remove the zero:
-3y = -1x

Add '3y' to each side of the equation.
-3y + 3y = -1x + 3y

Combine like terms: -3y + 3y = 0
0 = -1x + 3y

Simplifying
0 = -1x + 3y

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 3
Set the factor '(3x + -1y)' equal to zero and attempt to solve:

Simplifying
3x + -1y = 0

Solving
3x + -1y = 0

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

Add '-3x' to each side of the equation.
3x + -3x + -1y = 0 + -3x

Combine like terms: 3x + -3x = 0
0 + -1y = 0 + -3x
-1y = 0 + -3x
Remove the zero:
-1y = -3x

Add 'y' to each side of the equation.
-1y + y = -3x + y

Combine like terms: -1y + y = 0
0 = -3x + y

Simplifying
0 = -3x + y

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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