(3x+4y+1)dx+(x-5y+3)dy=0

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Solution for (3x+4y+1)dx+(x-5y+3)dy=0 equation: 


Simplifying
(3x + 4y + 1) * dx + (x + -5y + 3) * dy = 0

Reorder the terms:
(1 + 3x + 4y) * dx + (x + -5y + 3) * dy = 0

Reorder the terms for easier multiplication:
dx(1 + 3x + 4y) + (x + -5y + 3) * dy = 0
(1 * dx + 3x * dx + 4y * dx) + (x + -5y + 3) * dy = 0

Reorder the terms:
(1dx + 4dxy + 3dx2) + (x + -5y + 3) * dy = 0
(1dx + 4dxy + 3dx2) + (x + -5y + 3) * dy = 0

Reorder the terms:
1dx + 4dxy + 3dx2 + (3 + x + -5y) * dy = 0

Reorder the terms for easier multiplication:
1dx + 4dxy + 3dx2 + dy(3 + x + -5y) = 0
1dx + 4dxy + 3dx2 + (3 * dy + x * dy + -5y * dy) = 0

Reorder the terms:
1dx + 4dxy + 3dx2 + (dxy + 3dy + -5dy2) = 0
1dx + 4dxy + 3dx2 + (dxy + 3dy + -5dy2) = 0

Reorder the terms:
1dx + 4dxy + dxy + 3dx2 + 3dy + -5dy2 = 0

Combine like terms: 4dxy + dxy = 5dxy
1dx + 5dxy + 3dx2 + 3dy + -5dy2 = 0

Solving
1dx + 5dxy + 3dx2 + 3dy + -5dy2 = 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 + 3x2 + 3y + -5y2) = 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 + 3x2 + 3y + -5y2)' equal to zero and attempt to solve:

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

Solving
x + 5xy + 3x2 + 3y + -5y2 = 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 + 3x2 + 3y + -1x + -5y2 = 0 + -1x

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

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

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

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

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

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

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

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

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

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

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

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

Simplifying
0 = -1x + -5xy + -3x2 + -3y + 5y2

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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