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

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


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

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

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

Reorder the terms:
(-1dx + 3dxy + 2dx2) + (x + 2y) * dy = 0
(-1dx + 3dxy + 2dx2) + (x + 2y) * dy = 0

Reorder the terms for easier multiplication:
-1dx + 3dxy + 2dx2 + dy(x + 2y) = 0
-1dx + 3dxy + 2dx2 + (x * dy + 2y * dy) = 0
-1dx + 3dxy + 2dx2 + (dxy + 2dy2) = 0

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

Combine like terms: 3dxy + dxy = 4dxy
-1dx + 4dxy + 2dx2 + 2dy2 = 0

Solving
-1dx + 4dxy + 2dx2 + 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 + 4xy + 2x2 + 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 + 4xy + 2x2 + 2y2)' equal to zero and attempt to solve:

Simplifying
-1x + 4xy + 2x2 + 2y2 = 0

Solving
-1x + 4xy + 2x2 + 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 + 4xy + 2x2 + x + 2y2 = 0 + x

Reorder the terms:
-1x + x + 4xy + 2x2 + 2y2 = 0 + x

Combine like terms: -1x + x = 0
0 + 4xy + 2x2 + 2y2 = 0 + x
4xy + 2x2 + 2y2 = 0 + x
Remove the zero:
4xy + 2x2 + 2y2 = x

Add '-4xy' to each side of the equation.
4xy + 2x2 + -4xy + 2y2 = x + -4xy

Reorder the terms:
4xy + -4xy + 2x2 + 2y2 = x + -4xy

Combine like terms: 4xy + -4xy = 0
0 + 2x2 + 2y2 = x + -4xy
2x2 + 2y2 = x + -4xy

Add '-2x2' to each side of the equation.
2x2 + -2x2 + 2y2 = x + -4xy + -2x2

Combine like terms: 2x2 + -2x2 = 0
0 + 2y2 = x + -4xy + -2x2
2y2 = x + -4xy + -2x2

Add '-2y2' to each side of the equation.
2y2 + -2y2 = x + -4xy + -2x2 + -2y2

Combine like terms: 2y2 + -2y2 = 0
0 = x + -4xy + -2x2 + -2y2

Simplifying
0 = x + -4xy + -2x2 + -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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