(2x+3y-2)dx+(3x-4y+1)dy=0

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Solution for (2x+3y-2)dx+(3x-4y+1)dy=0 equation: 


Simplifying
(2x + 3y + -2) * dx + (3x + -4y + 1) * dy = 0

Reorder the terms:
(-2 + 2x + 3y) * dx + (3x + -4y + 1) * dy = 0

Reorder the terms for easier multiplication:
dx(-2 + 2x + 3y) + (3x + -4y + 1) * dy = 0
(-2 * dx + 2x * dx + 3y * dx) + (3x + -4y + 1) * dy = 0

Reorder the terms:
(-2dx + 3dxy + 2dx2) + (3x + -4y + 1) * dy = 0
(-2dx + 3dxy + 2dx2) + (3x + -4y + 1) * dy = 0

Reorder the terms:
-2dx + 3dxy + 2dx2 + (1 + 3x + -4y) * dy = 0

Reorder the terms for easier multiplication:
-2dx + 3dxy + 2dx2 + dy(1 + 3x + -4y) = 0
-2dx + 3dxy + 2dx2 + (1 * dy + 3x * dy + -4y * dy) = 0

Reorder the terms:
-2dx + 3dxy + 2dx2 + (3dxy + 1dy + -4dy2) = 0
-2dx + 3dxy + 2dx2 + (3dxy + 1dy + -4dy2) = 0

Reorder the terms:
-2dx + 3dxy + 3dxy + 2dx2 + 1dy + -4dy2 = 0

Combine like terms: 3dxy + 3dxy = 6dxy
-2dx + 6dxy + 2dx2 + 1dy + -4dy2 = 0

Solving
-2dx + 6dxy + 2dx2 + 1dy + -4dy2 = 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(-2x + 6xy + 2x2 + y + -4y2) = 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 '(-2x + 6xy + 2x2 + y + -4y2)' equal to zero and attempt to solve:

Simplifying
-2x + 6xy + 2x2 + y + -4y2 = 0

Solving
-2x + 6xy + 2x2 + y + -4y2 = 0

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

Add '2x' to each side of the equation.
-2x + 6xy + 2x2 + y + 2x + -4y2 = 0 + 2x

Reorder the terms:
-2x + 2x + 6xy + 2x2 + y + -4y2 = 0 + 2x

Combine like terms: -2x + 2x = 0
0 + 6xy + 2x2 + y + -4y2 = 0 + 2x
6xy + 2x2 + y + -4y2 = 0 + 2x
Remove the zero:
6xy + 2x2 + y + -4y2 = 2x

Add '-6xy' to each side of the equation.
6xy + 2x2 + y + -6xy + -4y2 = 2x + -6xy

Reorder the terms:
6xy + -6xy + 2x2 + y + -4y2 = 2x + -6xy

Combine like terms: 6xy + -6xy = 0
0 + 2x2 + y + -4y2 = 2x + -6xy
2x2 + y + -4y2 = 2x + -6xy

Add '-2x2' to each side of the equation.
2x2 + y + -2x2 + -4y2 = 2x + -6xy + -2x2

Reorder the terms:
2x2 + -2x2 + y + -4y2 = 2x + -6xy + -2x2

Combine like terms: 2x2 + -2x2 = 0
0 + y + -4y2 = 2x + -6xy + -2x2
y + -4y2 = 2x + -6xy + -2x2

Add '-1y' to each side of the equation.
y + -1y + -4y2 = 2x + -6xy + -2x2 + -1y

Combine like terms: y + -1y = 0
0 + -4y2 = 2x + -6xy + -2x2 + -1y
-4y2 = 2x + -6xy + -2x2 + -1y

Add '4y2' to each side of the equation.
-4y2 + 4y2 = 2x + -6xy + -2x2 + -1y + 4y2

Combine like terms: -4y2 + 4y2 = 0
0 = 2x + -6xy + -2x2 + -1y + 4y2

Simplifying
0 = 2x + -6xy + -2x2 + -1y + 4y2

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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