(3y+5)dx+(7x+2)dy=0

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Solution for (3y+5)dx+(7x+2)dy=0 equation: 


Simplifying
(3y + 5) * dx + (7x + 2) * dy = 0

Reorder the terms:
(5 + 3y) * dx + (7x + 2) * dy = 0

Reorder the terms for easier multiplication:
dx(5 + 3y) + (7x + 2) * dy = 0
(5 * dx + 3y * dx) + (7x + 2) * dy = 0
(5dx + 3dxy) + (7x + 2) * dy = 0

Reorder the terms:
5dx + 3dxy + (2 + 7x) * dy = 0

Reorder the terms for easier multiplication:
5dx + 3dxy + dy(2 + 7x) = 0
5dx + 3dxy + (2 * dy + 7x * dy) = 0

Reorder the terms:
5dx + 3dxy + (7dxy + 2dy) = 0
5dx + 3dxy + (7dxy + 2dy) = 0

Combine like terms: 3dxy + 7dxy = 10dxy
5dx + 10dxy + 2dy = 0

Solving
5dx + 10dxy + 2dy = 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 + 10xy + 2y) = 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 + 10xy + 2y)' equal to zero and attempt to solve:

Simplifying
5x + 10xy + 2y = 0

Solving
5x + 10xy + 2y = 0

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

Add '-5x' to each side of the equation.
5x + 10xy + -5x + 2y = 0 + -5x

Reorder the terms:
5x + -5x + 10xy + 2y = 0 + -5x

Combine like terms: 5x + -5x = 0
0 + 10xy + 2y = 0 + -5x
10xy + 2y = 0 + -5x
Remove the zero:
10xy + 2y = -5x

Add '-10xy' to each side of the equation.
10xy + -10xy + 2y = -5x + -10xy

Combine like terms: 10xy + -10xy = 0
0 + 2y = -5x + -10xy
2y = -5x + -10xy

Add '-2y' to each side of the equation.
2y + -2y = -5x + -10xy + -2y

Combine like terms: 2y + -2y = 0
0 = -5x + -10xy + -2y

Simplifying
0 = -5x + -10xy + -2y

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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