(3x-2y-3)DX+(6x-4y+1)dy=0

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Solution for (3x-2y-3)DX+(6x-4y+1)dy=0 equation: 


Simplifying
(3x + -2y + -3) * DX + (6x + -4y + 1) * dy = 0

Reorder the terms:
(-3 + 3x + -2y) * DX + (6x + -4y + 1) * dy = 0

Reorder the terms for easier multiplication:
DX(-3 + 3x + -2y) + (6x + -4y + 1) * dy = 0
(-3 * DX + 3x * DX + -2y * DX) + (6x + -4y + 1) * dy = 0
(-3DX + 3xDX + -2yDX) + (6x + -4y + 1) * dy = 0

Reorder the terms:
-3DX + 3xDX + -2yDX + (1 + 6x + -4y) * dy = 0

Reorder the terms for easier multiplication:
-3DX + 3xDX + -2yDX + dy(1 + 6x + -4y) = 0
-3DX + 3xDX + -2yDX + (1 * dy + 6x * dy + -4y * dy) = 0

Reorder the terms:
-3DX + 3xDX + -2yDX + (6dxy + 1dy + -4dy2) = 0
-3DX + 3xDX + -2yDX + (6dxy + 1dy + -4dy2) = 0

Reorder the terms:
-3DX + 6dxy + 1dy + -4dy2 + 3xDX + -2yDX = 0

Solving
-3DX + 6dxy + 1dy + -4dy2 + 3xDX + -2yDX = 0

Solving for variable 'D'.

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

Add '-6dxy' to each side of the equation.
-3DX + 6dxy + 1dy + -4dy2 + 3xDX + -6dxy + -2yDX = 0 + -6dxy

Reorder the terms:
-3DX + 6dxy + -6dxy + 1dy + -4dy2 + 3xDX + -2yDX = 0 + -6dxy

Combine like terms: 6dxy + -6dxy = 0
-3DX + 0 + 1dy + -4dy2 + 3xDX + -2yDX = 0 + -6dxy
-3DX + 1dy + -4dy2 + 3xDX + -2yDX = 0 + -6dxy
Remove the zero:
-3DX + 1dy + -4dy2 + 3xDX + -2yDX = -6dxy

Add '-1dy' to each side of the equation.
-3DX + 1dy + -4dy2 + 3xDX + -1dy + -2yDX = -6dxy + -1dy

Reorder the terms:
-3DX + 1dy + -1dy + -4dy2 + 3xDX + -2yDX = -6dxy + -1dy

Combine like terms: 1dy + -1dy = 0
-3DX + 0 + -4dy2 + 3xDX + -2yDX = -6dxy + -1dy
-3DX + -4dy2 + 3xDX + -2yDX = -6dxy + -1dy

Add '4dy2' to each side of the equation.
-3DX + -4dy2 + 3xDX + 4dy2 + -2yDX = -6dxy + -1dy + 4dy2

Reorder the terms:
-3DX + -4dy2 + 4dy2 + 3xDX + -2yDX = -6dxy + -1dy + 4dy2

Combine like terms: -4dy2 + 4dy2 = 0
-3DX + 0 + 3xDX + -2yDX = -6dxy + -1dy + 4dy2
-3DX + 3xDX + -2yDX = -6dxy + -1dy + 4dy2

Reorder the terms:
-3DX + 6dxy + dy + -4dy2 + 3xDX + -2yDX = -6dxy + -1dy + 4dy2 + 6dxy + dy + -4dy2

Reorder the terms:
-3DX + 6dxy + dy + -4dy2 + 3xDX + -2yDX = -6dxy + 6dxy + -1dy + dy + 4dy2 + -4dy2

Combine like terms: -6dxy + 6dxy = 0
-3DX + 6dxy + dy + -4dy2 + 3xDX + -2yDX = 0 + -1dy + dy + 4dy2 + -4dy2
-3DX + 6dxy + dy + -4dy2 + 3xDX + -2yDX = -1dy + dy + 4dy2 + -4dy2

Combine like terms: -1dy + dy = 0
-3DX + 6dxy + dy + -4dy2 + 3xDX + -2yDX = 0 + 4dy2 + -4dy2
-3DX + 6dxy + dy + -4dy2 + 3xDX + -2yDX = 4dy2 + -4dy2

Combine like terms: 4dy2 + -4dy2 = 0
-3DX + 6dxy + dy + -4dy2 + 3xDX + -2yDX = 0

The solution to this equation could not be determined.

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