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

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


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

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

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

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

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

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

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

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

Combine like terms: 4dxy + 4dxy = 8dxy
5dx + 8dxy + 3dx2 + 3dy + -3dy2 = 0

Solving
5dx + 8dxy + 3dx2 + 3dy + -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 + 8xy + 3x2 + 3y + -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 + 8xy + 3x2 + 3y + -3y2)' equal to zero and attempt to solve:

Simplifying
5x + 8xy + 3x2 + 3y + -3y2 = 0

Solving
5x + 8xy + 3x2 + 3y + -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 + 8xy + 3x2 + 3y + -5x + -3y2 = 0 + -5x

Reorder the terms:
5x + -5x + 8xy + 3x2 + 3y + -3y2 = 0 + -5x

Combine like terms: 5x + -5x = 0
0 + 8xy + 3x2 + 3y + -3y2 = 0 + -5x
8xy + 3x2 + 3y + -3y2 = 0 + -5x
Remove the zero:
8xy + 3x2 + 3y + -3y2 = -5x

Add '-8xy' to each side of the equation.
8xy + 3x2 + 3y + -8xy + -3y2 = -5x + -8xy

Reorder the terms:
8xy + -8xy + 3x2 + 3y + -3y2 = -5x + -8xy

Combine like terms: 8xy + -8xy = 0
0 + 3x2 + 3y + -3y2 = -5x + -8xy
3x2 + 3y + -3y2 = -5x + -8xy

Add '-3x2' to each side of the equation.
3x2 + 3y + -3x2 + -3y2 = -5x + -8xy + -3x2

Reorder the terms:
3x2 + -3x2 + 3y + -3y2 = -5x + -8xy + -3x2

Combine like terms: 3x2 + -3x2 = 0
0 + 3y + -3y2 = -5x + -8xy + -3x2
3y + -3y2 = -5x + -8xy + -3x2

Add '-3y' to each side of the equation.
3y + -3y + -3y2 = -5x + -8xy + -3x2 + -3y

Combine like terms: 3y + -3y = 0
0 + -3y2 = -5x + -8xy + -3x2 + -3y
-3y2 = -5x + -8xy + -3x2 + -3y

Add '3y2' to each side of the equation.
-3y2 + 3y2 = -5x + -8xy + -3x2 + -3y + 3y2

Combine like terms: -3y2 + 3y2 = 0
0 = -5x + -8xy + -3x2 + -3y + 3y2

Simplifying
0 = -5x + -8xy + -3x2 + -3y + 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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