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

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


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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Simplifying
0 = -1x + -2x2 + 2y + -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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