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

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


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

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

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

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

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

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

Combine like terms: 2dxy + 3dxy = 5dxy
-1dx + 5dxy + 3dx2 + 2dy2 = 0

Solving
-1dx + 5dxy + 3dx2 + 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(-1x + 5xy + 3x2 + 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 '(-1x + 5xy + 3x2 + 2y2)' equal to zero and attempt to solve:

Simplifying
-1x + 5xy + 3x2 + 2y2 = 0

Solving
-1x + 5xy + 3x2 + 2y2 = 0

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

Add 'x' to each side of the equation.
-1x + 5xy + 3x2 + x + 2y2 = 0 + x

Reorder the terms:
-1x + x + 5xy + 3x2 + 2y2 = 0 + x

Combine like terms: -1x + x = 0
0 + 5xy + 3x2 + 2y2 = 0 + x
5xy + 3x2 + 2y2 = 0 + x
Remove the zero:
5xy + 3x2 + 2y2 = x

Add '-5xy' to each side of the equation.
5xy + 3x2 + -5xy + 2y2 = x + -5xy

Reorder the terms:
5xy + -5xy + 3x2 + 2y2 = x + -5xy

Combine like terms: 5xy + -5xy = 0
0 + 3x2 + 2y2 = x + -5xy
3x2 + 2y2 = x + -5xy

Add '-3x2' to each side of the equation.
3x2 + -3x2 + 2y2 = x + -5xy + -3x2

Combine like terms: 3x2 + -3x2 = 0
0 + 2y2 = x + -5xy + -3x2
2y2 = x + -5xy + -3x2

Add '-2y2' to each side of the equation.
2y2 + -2y2 = x + -5xy + -3x2 + -2y2

Combine like terms: 2y2 + -2y2 = 0
0 = x + -5xy + -3x2 + -2y2

Simplifying
0 = x + -5xy + -3x2 + -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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