(X-6y+2)DX+2(x+2y+2)dy=0

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


Simplifying
(X + -6y + 2) * DX + 2(x + 2y + 2) * dy = 0

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

Reorder the terms for easier multiplication:
DX(2 + X + -6y) + 2(x + 2y + 2) * dy = 0
(2 * DX + X * DX + -6y * DX) + 2(x + 2y + 2) * dy = 0
(2DX + DX2 + -6yDX) + 2(x + 2y + 2) * dy = 0

Reorder the terms:
2DX + DX2 + -6yDX + 2(2 + x + 2y) * dy = 0

Reorder the terms for easier multiplication:
2DX + DX2 + -6yDX + 2dy(2 + x + 2y) = 0
2DX + DX2 + -6yDX + (2 * 2dy + x * 2dy + 2y * 2dy) = 0

Reorder the terms:
2DX + DX2 + -6yDX + (2dxy + 4dy + 4dy2) = 0
2DX + DX2 + -6yDX + (2dxy + 4dy + 4dy2) = 0

Reorder the terms:
2DX + DX2 + 2dxy + 4dy + 4dy2 + -6yDX = 0

Solving
2DX + DX2 + 2dxy + 4dy + 4dy2 + -6yDX = 0

Solving for variable 'D'.

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

Add '-2dxy' to each side of the equation.
2DX + DX2 + 2dxy + 4dy + 4dy2 + -2dxy + -6yDX = 0 + -2dxy

Reorder the terms:
2DX + DX2 + 2dxy + -2dxy + 4dy + 4dy2 + -6yDX = 0 + -2dxy

Combine like terms: 2dxy + -2dxy = 0
2DX + DX2 + 0 + 4dy + 4dy2 + -6yDX = 0 + -2dxy
2DX + DX2 + 4dy + 4dy2 + -6yDX = 0 + -2dxy
Remove the zero:
2DX + DX2 + 4dy + 4dy2 + -6yDX = -2dxy

Add '-4dy' to each side of the equation.
2DX + DX2 + 4dy + 4dy2 + -4dy + -6yDX = -2dxy + -4dy

Reorder the terms:
2DX + DX2 + 4dy + -4dy + 4dy2 + -6yDX = -2dxy + -4dy

Combine like terms: 4dy + -4dy = 0
2DX + DX2 + 0 + 4dy2 + -6yDX = -2dxy + -4dy
2DX + DX2 + 4dy2 + -6yDX = -2dxy + -4dy

Add '-4dy2' to each side of the equation.
2DX + DX2 + 4dy2 + -4dy2 + -6yDX = -2dxy + -4dy + -4dy2

Combine like terms: 4dy2 + -4dy2 = 0
2DX + DX2 + 0 + -6yDX = -2dxy + -4dy + -4dy2
2DX + DX2 + -6yDX = -2dxy + -4dy + -4dy2

Reorder the terms:
2DX + DX2 + 2dxy + 4dy + 4dy2 + -6yDX = -2dxy + -4dy + -4dy2 + 2dxy + 4dy + 4dy2

Reorder the terms:
2DX + DX2 + 2dxy + 4dy + 4dy2 + -6yDX = -2dxy + 2dxy + -4dy + 4dy + -4dy2 + 4dy2

Combine like terms: -2dxy + 2dxy = 0
2DX + DX2 + 2dxy + 4dy + 4dy2 + -6yDX = 0 + -4dy + 4dy + -4dy2 + 4dy2
2DX + DX2 + 2dxy + 4dy + 4dy2 + -6yDX = -4dy + 4dy + -4dy2 + 4dy2

Combine like terms: -4dy + 4dy = 0
2DX + DX2 + 2dxy + 4dy + 4dy2 + -6yDX = 0 + -4dy2 + 4dy2
2DX + DX2 + 2dxy + 4dy + 4dy2 + -6yDX = -4dy2 + 4dy2

Combine like terms: -4dy2 + 4dy2 = 0
2DX + DX2 + 2dxy + 4dy + 4dy2 + -6yDX = 0

The solution to this equation could not be determined.

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