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

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


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

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

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

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

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

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

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

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

Combine like terms: 2dxy + 2dxy = 4dxy
5dx + 4dxy + 3dx2 + -5dy + 3dy2 = 0

Solving
5dx + 4dxy + 3dx2 + -5dy + 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(5x + 4xy + 3x2 + -5y + 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 '(5x + 4xy + 3x2 + -5y + 3y2)' equal to zero and attempt to solve:

Simplifying
5x + 4xy + 3x2 + -5y + 3y2 = 0

Solving
5x + 4xy + 3x2 + -5y + 3y2 = 0

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

Add '-5x' to each side of the equation.
5x + 4xy + 3x2 + -5y + -5x + 3y2 = 0 + -5x

Reorder the terms:
5x + -5x + 4xy + 3x2 + -5y + 3y2 = 0 + -5x

Combine like terms: 5x + -5x = 0
0 + 4xy + 3x2 + -5y + 3y2 = 0 + -5x
4xy + 3x2 + -5y + 3y2 = 0 + -5x
Remove the zero:
4xy + 3x2 + -5y + 3y2 = -5x

Add '-4xy' to each side of the equation.
4xy + 3x2 + -5y + -4xy + 3y2 = -5x + -4xy

Reorder the terms:
4xy + -4xy + 3x2 + -5y + 3y2 = -5x + -4xy

Combine like terms: 4xy + -4xy = 0
0 + 3x2 + -5y + 3y2 = -5x + -4xy
3x2 + -5y + 3y2 = -5x + -4xy

Add '-3x2' to each side of the equation.
3x2 + -5y + -3x2 + 3y2 = -5x + -4xy + -3x2

Reorder the terms:
3x2 + -3x2 + -5y + 3y2 = -5x + -4xy + -3x2

Combine like terms: 3x2 + -3x2 = 0
0 + -5y + 3y2 = -5x + -4xy + -3x2
-5y + 3y2 = -5x + -4xy + -3x2

Add '5y' to each side of the equation.
-5y + 5y + 3y2 = -5x + -4xy + -3x2 + 5y

Combine like terms: -5y + 5y = 0
0 + 3y2 = -5x + -4xy + -3x2 + 5y
3y2 = -5x + -4xy + -3x2 + 5y

Add '-3y2' to each side of the equation.
3y2 + -3y2 = -5x + -4xy + -3x2 + 5y + -3y2

Combine like terms: 3y2 + -3y2 = 0
0 = -5x + -4xy + -3x2 + 5y + -3y2

Simplifying
0 = -5x + -4xy + -3x2 + 5y + -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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