(2x+1)dy+(3y+2)dx=0

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Solution for (2x+1)dy+(3y+2)dx=0 equation: 


Simplifying
(2x + 1) * dy + (3y + 2) * dx = 0

Reorder the terms:
(1 + 2x) * dy + (3y + 2) * dx = 0

Reorder the terms for easier multiplication:
dy(1 + 2x) + (3y + 2) * dx = 0
(1 * dy + 2x * dy) + (3y + 2) * dx = 0

Reorder the terms:
(2dxy + 1dy) + (3y + 2) * dx = 0
(2dxy + 1dy) + (3y + 2) * dx = 0

Reorder the terms:
2dxy + 1dy + (2 + 3y) * dx = 0

Reorder the terms for easier multiplication:
2dxy + 1dy + dx(2 + 3y) = 0
2dxy + 1dy + (2 * dx + 3y * dx) = 0
2dxy + 1dy + (2dx + 3dxy) = 0

Reorder the terms:
2dx + 2dxy + 3dxy + 1dy = 0

Combine like terms: 2dxy + 3dxy = 5dxy
2dx + 5dxy + 1dy = 0

Solving
2dx + 5dxy + 1dy = 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(2x + 5xy + y) = 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 '(2x + 5xy + y)' equal to zero and attempt to solve:

Simplifying
2x + 5xy + y = 0

Solving
2x + 5xy + y = 0

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

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

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

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

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

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

Add '-1y' to each side of the equation.
y + -1y = -2x + -5xy + -1y

Combine like terms: y + -1y = 0
0 = -2x + -5xy + -1y

Simplifying
0 = -2x + -5xy + -1y

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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