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

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


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

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

Remove parenthesis around (6 + 3x + -1y)
6 + 3x + -1y + (6x + -2y + -6) * dy = 0

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

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

Reorder the terms:
6 + 3x + -1y + (6dxy + -6dy + -2dy2) = 0
6 + 3x + -1y + (6dxy + -6dy + -2dy2) = 0

Reorder the terms:
6 + 6dxy + -6dy + -2dy2 + 3x + -1y = 0

Solving
6 + 6dxy + -6dy + -2dy2 + 3x + -1y = 0

Solving for variable 'd'.

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

Add '-6' to each side of the equation.
6 + 6dxy + -6dy + -2dy2 + 3x + -6 + -1y = 0 + -6

Reorder the terms:
6 + -6 + 6dxy + -6dy + -2dy2 + 3x + -1y = 0 + -6

Combine like terms: 6 + -6 = 0
0 + 6dxy + -6dy + -2dy2 + 3x + -1y = 0 + -6
6dxy + -6dy + -2dy2 + 3x + -1y = 0 + -6

Combine like terms: 0 + -6 = -6
6dxy + -6dy + -2dy2 + 3x + -1y = -6

Add '-3x' to each side of the equation.
6dxy + -6dy + -2dy2 + 3x + -3x + -1y = -6 + -3x

Combine like terms: 3x + -3x = 0
6dxy + -6dy + -2dy2 + 0 + -1y = -6 + -3x
6dxy + -6dy + -2dy2 + -1y = -6 + -3x

Add 'y' to each side of the equation.
6dxy + -6dy + -2dy2 + -1y + y = -6 + -3x + y

Combine like terms: -1y + y = 0
6dxy + -6dy + -2dy2 + 0 = -6 + -3x + y
6dxy + -6dy + -2dy2 = -6 + -3x + y

Reorder the terms:
6 + 6dxy + -6dy + -2dy2 + 3x + -1y = -6 + -3x + y + 6 + 3x + -1y

Reorder the terms:
6 + 6dxy + -6dy + -2dy2 + 3x + -1y = -6 + 6 + -3x + 3x + y + -1y

Combine like terms: -6 + 6 = 0
6 + 6dxy + -6dy + -2dy2 + 3x + -1y = 0 + -3x + 3x + y + -1y
6 + 6dxy + -6dy + -2dy2 + 3x + -1y = -3x + 3x + y + -1y

Combine like terms: -3x + 3x = 0
6 + 6dxy + -6dy + -2dy2 + 3x + -1y = 0 + y + -1y
6 + 6dxy + -6dy + -2dy2 + 3x + -1y = y + -1y

Combine like terms: y + -1y = 0
6 + 6dxy + -6dy + -2dy2 + 3x + -1y = 0

The solution to this equation could not be determined.

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