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

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


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

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

Reorder the terms:
(dxy + dx2) + (2x + 2y + -1) * dy = 0
(dxy + dx2) + (2x + 2y + -1) * dy = 0

Reorder the terms:
dxy + dx2 + (-1 + 2x + 2y) * dy = 0

Reorder the terms for easier multiplication:
dxy + dx2 + dy(-1 + 2x + 2y) = 0
dxy + dx2 + (-1 * dy + 2x * dy + 2y * dy) = 0

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

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

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

Solving
3dxy + dx2 + -1dy + 2dy2 = 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(3xy + x2 + -1y + 2y2) = 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 '(3xy + x2 + -1y + 2y2)' equal to zero and attempt to solve:

Simplifying
3xy + x2 + -1y + 2y2 = 0

Solving
3xy + x2 + -1y + 2y2 = 0

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

Add '-3xy' to each side of the equation.
3xy + x2 + -1y + -3xy + 2y2 = 0 + -3xy

Reorder the terms:
3xy + -3xy + x2 + -1y + 2y2 = 0 + -3xy

Combine like terms: 3xy + -3xy = 0
0 + x2 + -1y + 2y2 = 0 + -3xy
x2 + -1y + 2y2 = 0 + -3xy
Remove the zero:
x2 + -1y + 2y2 = -3xy

Add '-1x2' to each side of the equation.
x2 + -1y + -1x2 + 2y2 = -3xy + -1x2

Reorder the terms:
x2 + -1x2 + -1y + 2y2 = -3xy + -1x2

Combine like terms: x2 + -1x2 = 0
0 + -1y + 2y2 = -3xy + -1x2
-1y + 2y2 = -3xy + -1x2

Add 'y' to each side of the equation.
-1y + y + 2y2 = -3xy + -1x2 + y

Combine like terms: -1y + y = 0
0 + 2y2 = -3xy + -1x2 + y
2y2 = -3xy + -1x2 + y

Add '-2y2' to each side of the equation.
2y2 + -2y2 = -3xy + -1x2 + y + -2y2

Combine like terms: 2y2 + -2y2 = 0
0 = -3xy + -1x2 + y + -2y2

Simplifying
0 = -3xy + -1x2 + y + -2y2

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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