(3x+4y-1)dy+(2x+3y+1)dx=0

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Solution for (3x+4y-1)dy+(2x+3y+1)dx=0 equation: 


Simplifying
(3x + 4y + -1) * dy + (2x + 3y + 1) * dx = 0

Reorder the terms:
(-1 + 3x + 4y) * dy + (2x + 3y + 1) * dx = 0

Reorder the terms for easier multiplication:
dy(-1 + 3x + 4y) + (2x + 3y + 1) * dx = 0
(-1 * dy + 3x * dy + 4y * dy) + (2x + 3y + 1) * dx = 0

Reorder the terms:
(3dxy + -1dy + 4dy2) + (2x + 3y + 1) * dx = 0
(3dxy + -1dy + 4dy2) + (2x + 3y + 1) * dx = 0

Reorder the terms:
3dxy + -1dy + 4dy2 + (1 + 2x + 3y) * dx = 0

Reorder the terms for easier multiplication:
3dxy + -1dy + 4dy2 + dx(1 + 2x + 3y) = 0
3dxy + -1dy + 4dy2 + (1 * dx + 2x * dx + 3y * dx) = 0

Reorder the terms:
3dxy + -1dy + 4dy2 + (1dx + 3dxy + 2dx2) = 0
3dxy + -1dy + 4dy2 + (1dx + 3dxy + 2dx2) = 0

Reorder the terms:
1dx + 3dxy + 3dxy + 2dx2 + -1dy + 4dy2 = 0

Combine like terms: 3dxy + 3dxy = 6dxy
1dx + 6dxy + 2dx2 + -1dy + 4dy2 = 0

Solving
1dx + 6dxy + 2dx2 + -1dy + 4dy2 = 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 + 6xy + 2x2 + -1y + 4y2) = 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 + 6xy + 2x2 + -1y + 4y2)' equal to zero and attempt to solve:

Simplifying
x + 6xy + 2x2 + -1y + 4y2 = 0

Solving
x + 6xy + 2x2 + -1y + 4y2 = 0

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

Add '-1x' to each side of the equation.
x + 6xy + 2x2 + -1y + -1x + 4y2 = 0 + -1x

Reorder the terms:
x + -1x + 6xy + 2x2 + -1y + 4y2 = 0 + -1x

Combine like terms: x + -1x = 0
0 + 6xy + 2x2 + -1y + 4y2 = 0 + -1x
6xy + 2x2 + -1y + 4y2 = 0 + -1x
Remove the zero:
6xy + 2x2 + -1y + 4y2 = -1x

Add '-6xy' to each side of the equation.
6xy + 2x2 + -1y + -6xy + 4y2 = -1x + -6xy

Reorder the terms:
6xy + -6xy + 2x2 + -1y + 4y2 = -1x + -6xy

Combine like terms: 6xy + -6xy = 0
0 + 2x2 + -1y + 4y2 = -1x + -6xy
2x2 + -1y + 4y2 = -1x + -6xy

Add '-2x2' to each side of the equation.
2x2 + -1y + -2x2 + 4y2 = -1x + -6xy + -2x2

Reorder the terms:
2x2 + -2x2 + -1y + 4y2 = -1x + -6xy + -2x2

Combine like terms: 2x2 + -2x2 = 0
0 + -1y + 4y2 = -1x + -6xy + -2x2
-1y + 4y2 = -1x + -6xy + -2x2

Add 'y' to each side of the equation.
-1y + y + 4y2 = -1x + -6xy + -2x2 + y

Combine like terms: -1y + y = 0
0 + 4y2 = -1x + -6xy + -2x2 + y
4y2 = -1x + -6xy + -2x2 + y

Add '-4y2' to each side of the equation.
4y2 + -4y2 = -1x + -6xy + -2x2 + y + -4y2

Combine like terms: 4y2 + -4y2 = 0
0 = -1x + -6xy + -2x2 + y + -4y2

Simplifying
0 = -1x + -6xy + -2x2 + y + -4y2

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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