(2x-3y-8)dy+(-x-3y-5)dx=0

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Solution for (2x-3y-8)dy+(-x-3y-5)dx=0 equation:


Simplifying
(2x + -3y + -8) * dy + (-1x + -3y + -5) * dx = 0

Reorder the terms:
(-8 + 2x + -3y) * dy + (-1x + -3y + -5) * dx = 0

Reorder the terms for easier multiplication:
dy(-8 + 2x + -3y) + (-1x + -3y + -5) * dx = 0
(-8 * dy + 2x * dy + -3y * dy) + (-1x + -3y + -5) * dx = 0

Reorder the terms:
(2dxy + -8dy + -3dy2) + (-1x + -3y + -5) * dx = 0
(2dxy + -8dy + -3dy2) + (-1x + -3y + -5) * dx = 0

Reorder the terms:
2dxy + -8dy + -3dy2 + (-5 + -1x + -3y) * dx = 0

Reorder the terms for easier multiplication:
2dxy + -8dy + -3dy2 + dx(-5 + -1x + -3y) = 0
2dxy + -8dy + -3dy2 + (-5 * dx + -1x * dx + -3y * dx) = 0

Reorder the terms:
2dxy + -8dy + -3dy2 + (-5dx + -3dxy + -1dx2) = 0
2dxy + -8dy + -3dy2 + (-5dx + -3dxy + -1dx2) = 0

Reorder the terms:
-5dx + 2dxy + -3dxy + -1dx2 + -8dy + -3dy2 = 0

Combine like terms: 2dxy + -3dxy = -1dxy
-5dx + -1dxy + -1dx2 + -8dy + -3dy2 = 0

Solving
-5dx + -1dxy + -1dx2 + -8dy + -3dy2 = 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), '-1d'.
-1d(5x + xy + x2 + 8y + 3y2) = 0

Ignore the factor -1.

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 '(5x + xy + x2 + 8y + 3y2)' equal to zero and attempt to solve: Simplifying 5x + xy + x2 + 8y + 3y2 = 0 Solving 5x + xy + x2 + 8y + 3y2 = 0 Move all terms containing d to the left, all other terms to the right. Add '-5x' to each side of the equation. 5x + xy + x2 + 8y + -5x + 3y2 = 0 + -5x Reorder the terms: 5x + -5x + xy + x2 + 8y + 3y2 = 0 + -5x Combine like terms: 5x + -5x = 0 0 + xy + x2 + 8y + 3y2 = 0 + -5x xy + x2 + 8y + 3y2 = 0 + -5x Remove the zero: xy + x2 + 8y + 3y2 = -5x Add '-1xy' to each side of the equation. xy + x2 + 8y + -1xy + 3y2 = -5x + -1xy Reorder the terms: xy + -1xy + x2 + 8y + 3y2 = -5x + -1xy Combine like terms: xy + -1xy = 0 0 + x2 + 8y + 3y2 = -5x + -1xy x2 + 8y + 3y2 = -5x + -1xy Add '-1x2' to each side of the equation. x2 + 8y + -1x2 + 3y2 = -5x + -1xy + -1x2 Reorder the terms: x2 + -1x2 + 8y + 3y2 = -5x + -1xy + -1x2 Combine like terms: x2 + -1x2 = 0 0 + 8y + 3y2 = -5x + -1xy + -1x2 8y + 3y2 = -5x + -1xy + -1x2 Add '-8y' to each side of the equation. 8y + -8y + 3y2 = -5x + -1xy + -1x2 + -8y Combine like terms: 8y + -8y = 0 0 + 3y2 = -5x + -1xy + -1x2 + -8y 3y2 = -5x + -1xy + -1x2 + -8y Add '-3y2' to each side of the equation. 3y2 + -3y2 = -5x + -1xy + -1x2 + -8y + -3y2 Combine like terms: 3y2 + -3y2 = 0 0 = -5x + -1xy + -1x2 + -8y + -3y2 Simplifying 0 = -5x + -1xy + -1x2 + -8y + -3y2 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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