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

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


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

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

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

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

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

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

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

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

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

Solving
1dx + 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(x + 3xy + x2 + y + 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 '(x + 3xy + x2 + y + 2y2)' equal to zero and attempt to solve:

Simplifying
x + 3xy + x2 + y + 2y2 = 0

Solving
x + 3xy + x2 + y + 2y2 = 0

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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