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

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


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

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

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

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

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

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

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

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

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

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

Solving
4xy + x2 + -4y + 3y2 = 0

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

Add '-4xy' to each side of the equation.
4xy + x2 + -4y + -4xy + 3y2 = 0 + -4xy

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

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

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

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

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

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

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

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

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

Simplifying
0 = -4xy + -1x2 + 4y + -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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