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

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


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

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

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

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

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

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

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

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

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

Solving
4dx + 2dx2 + 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(4x + 2x2 + 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 '(4x + 2x2 + y + -2y2)' equal to zero and attempt to solve:

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

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

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

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

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

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

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

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

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

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

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

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

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

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