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

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


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

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

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

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

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

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

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

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

Combine like terms: 3dxy + 4dxy = 7dxy
1dx + 7dxy + 3dx2 + 1dy + -4dy2 = 0

Solving
1dx + 7dxy + 3dx2 + 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 + 7xy + 3x2 + y + -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 + 7xy + 3x2 + y + -4y2)' equal to zero and attempt to solve:

Simplifying
x + 7xy + 3x2 + y + -4y2 = 0

Solving
x + 7xy + 3x2 + y + -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 + 7xy + 3x2 + y + -1x + -4y2 = 0 + -1x

Reorder the terms:
x + -1x + 7xy + 3x2 + y + -4y2 = 0 + -1x

Combine like terms: x + -1x = 0
0 + 7xy + 3x2 + y + -4y2 = 0 + -1x
7xy + 3x2 + y + -4y2 = 0 + -1x
Remove the zero:
7xy + 3x2 + y + -4y2 = -1x

Add '-7xy' to each side of the equation.
7xy + 3x2 + y + -7xy + -4y2 = -1x + -7xy

Reorder the terms:
7xy + -7xy + 3x2 + y + -4y2 = -1x + -7xy

Combine like terms: 7xy + -7xy = 0
0 + 3x2 + y + -4y2 = -1x + -7xy
3x2 + y + -4y2 = -1x + -7xy

Add '-3x2' to each side of the equation.
3x2 + y + -3x2 + -4y2 = -1x + -7xy + -3x2

Reorder the terms:
3x2 + -3x2 + y + -4y2 = -1x + -7xy + -3x2

Combine like terms: 3x2 + -3x2 = 0
0 + y + -4y2 = -1x + -7xy + -3x2
y + -4y2 = -1x + -7xy + -3x2

Add '-1y' to each side of the equation.
y + -1y + -4y2 = -1x + -7xy + -3x2 + -1y

Combine like terms: y + -1y = 0
0 + -4y2 = -1x + -7xy + -3x2 + -1y
-4y2 = -1x + -7xy + -3x2 + -1y

Add '4y2' to each side of the equation.
-4y2 + 4y2 = -1x + -7xy + -3x2 + -1y + 4y2

Combine like terms: -4y2 + 4y2 = 0
0 = -1x + -7xy + -3x2 + -1y + 4y2

Simplifying
0 = -1x + -7xy + -3x2 + -1y + 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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