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

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


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

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

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

Reorder the terms:
(-1dx + -2dxy + dx2) + (3x + -6 + 2) * dy = 0
(-1dx + -2dxy + dx2) + (3x + -6 + 2) * dy = 0

Reorder the terms:
-1dx + -2dxy + dx2 + (-6 + 2 + 3x) * dy = 0

Combine like terms: -6 + 2 = -4
-1dx + -2dxy + dx2 + (-4 + 3x) * dy = 0

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

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

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

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

Solving
-1dx + 1dxy + dx2 + -4dy = 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(-1x + xy + x2 + -4y) = 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 '(-1x + xy + x2 + -4y)' equal to zero and attempt to solve: Simplifying -1x + xy + x2 + -4y = 0 Solving -1x + xy + x2 + -4y = 0 Move all terms containing d to the left, all other terms to the right. Add 'x' to each side of the equation. -1x + xy + x2 + x + -4y = 0 + x Reorder the terms: -1x + x + xy + x2 + -4y = 0 + x Combine like terms: -1x + x = 0 0 + xy + x2 + -4y = 0 + x xy + x2 + -4y = 0 + x Remove the zero: xy + x2 + -4y = x Add '-1xy' to each side of the equation. xy + x2 + -1xy + -4y = x + -1xy Reorder the terms: xy + -1xy + x2 + -4y = x + -1xy Combine like terms: xy + -1xy = 0 0 + x2 + -4y = x + -1xy x2 + -4y = x + -1xy Add '-1x2' to each side of the equation. x2 + -1x2 + -4y = x + -1xy + -1x2 Combine like terms: x2 + -1x2 = 0 0 + -4y = x + -1xy + -1x2 -4y = x + -1xy + -1x2 Add '4y' to each side of the equation. -4y + 4y = x + -1xy + -1x2 + 4y Combine like terms: -4y + 4y = 0 0 = x + -1xy + -1x2 + 4y Simplifying 0 = x + -1xy + -1x2 + 4y 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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