(2x+3y-5)dy+(2x+3y+1)dx=0

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Solution for (2x+3y-5)dy+(2x+3y+1)dx=0 equation: 


Simplifying
(2x + 3y + -5) * dy + (2x + 3y + 1) * dx = 0

Reorder the terms:
(-5 + 2x + 3y) * dy + (2x + 3y + 1) * dx = 0

Reorder the terms for easier multiplication:
dy(-5 + 2x + 3y) + (2x + 3y + 1) * dx = 0
(-5 * dy + 2x * dy + 3y * dy) + (2x + 3y + 1) * dx = 0

Reorder the terms:
(2dxy + -5dy + 3dy2) + (2x + 3y + 1) * dx = 0
(2dxy + -5dy + 3dy2) + (2x + 3y + 1) * dx = 0

Reorder the terms:
2dxy + -5dy + 3dy2 + (1 + 2x + 3y) * dx = 0

Reorder the terms for easier multiplication:
2dxy + -5dy + 3dy2 + dx(1 + 2x + 3y) = 0
2dxy + -5dy + 3dy2 + (1 * dx + 2x * dx + 3y * dx) = 0

Reorder the terms:
2dxy + -5dy + 3dy2 + (1dx + 3dxy + 2dx2) = 0
2dxy + -5dy + 3dy2 + (1dx + 3dxy + 2dx2) = 0

Reorder the terms:
1dx + 2dxy + 3dxy + 2dx2 + -5dy + 3dy2 = 0

Combine like terms: 2dxy + 3dxy = 5dxy
1dx + 5dxy + 2dx2 + -5dy + 3dy2 = 0

Solving
1dx + 5dxy + 2dx2 + -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(x + 5xy + 2x2 + -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 '(x + 5xy + 2x2 + -5y + 3y2)' equal to zero and attempt to solve:

Simplifying
x + 5xy + 2x2 + -5y + 3y2 = 0

Solving
x + 5xy + 2x2 + -5y + 3y2 = 0

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

Add '-1x' to each side of the equation.
x + 5xy + 2x2 + -5y + -1x + 3y2 = 0 + -1x

Reorder the terms:
x + -1x + 5xy + 2x2 + -5y + 3y2 = 0 + -1x

Combine like terms: x + -1x = 0
0 + 5xy + 2x2 + -5y + 3y2 = 0 + -1x
5xy + 2x2 + -5y + 3y2 = 0 + -1x
Remove the zero:
5xy + 2x2 + -5y + 3y2 = -1x

Add '-5xy' to each side of the equation.
5xy + 2x2 + -5y + -5xy + 3y2 = -1x + -5xy

Reorder the terms:
5xy + -5xy + 2x2 + -5y + 3y2 = -1x + -5xy

Combine like terms: 5xy + -5xy = 0
0 + 2x2 + -5y + 3y2 = -1x + -5xy
2x2 + -5y + 3y2 = -1x + -5xy

Add '-2x2' to each side of the equation.
2x2 + -5y + -2x2 + 3y2 = -1x + -5xy + -2x2

Reorder the terms:
2x2 + -2x2 + -5y + 3y2 = -1x + -5xy + -2x2

Combine like terms: 2x2 + -2x2 = 0
0 + -5y + 3y2 = -1x + -5xy + -2x2
-5y + 3y2 = -1x + -5xy + -2x2

Add '5y' to each side of the equation.
-5y + 5y + 3y2 = -1x + -5xy + -2x2 + 5y

Combine like terms: -5y + 5y = 0
0 + 3y2 = -1x + -5xy + -2x2 + 5y
3y2 = -1x + -5xy + -2x2 + 5y

Add '-3y2' to each side of the equation.
3y2 + -3y2 = -1x + -5xy + -2x2 + 5y + -3y2

Combine like terms: 3y2 + -3y2 = 0
0 = -1x + -5xy + -2x2 + 5y + -3y2

Simplifying
0 = -1x + -5xy + -2x2 + 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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