(4x-3y-18)dy-(2y-x-7)dx=0

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Solution for (4x-3y-18)dy-(2y-x-7)dx=0 equation:


Simplifying
(4x + -3y + -18) * dy + -1(2y + -1x + -7) * dx = 0

Reorder the terms:
(-18 + 4x + -3y) * dy + -1(2y + -1x + -7) * dx = 0

Reorder the terms for easier multiplication:
dy(-18 + 4x + -3y) + -1(2y + -1x + -7) * dx = 0
(-18 * dy + 4x * dy + -3y * dy) + -1(2y + -1x + -7) * dx = 0

Reorder the terms:
(4dxy + -18dy + -3dy2) + -1(2y + -1x + -7) * dx = 0
(4dxy + -18dy + -3dy2) + -1(2y + -1x + -7) * dx = 0

Reorder the terms:
4dxy + -18dy + -3dy2 + -1(-7 + -1x + 2y) * dx = 0

Reorder the terms for easier multiplication:
4dxy + -18dy + -3dy2 + -1dx(-7 + -1x + 2y) = 0
4dxy + -18dy + -3dy2 + (-7 * -1dx + -1x * -1dx + 2y * -1dx) = 0

Reorder the terms:
4dxy + -18dy + -3dy2 + (7dx + -2dxy + 1dx2) = 0
4dxy + -18dy + -3dy2 + (7dx + -2dxy + 1dx2) = 0

Reorder the terms:
7dx + 4dxy + -2dxy + 1dx2 + -18dy + -3dy2 = 0

Combine like terms: 4dxy + -2dxy = 2dxy
7dx + 2dxy + 1dx2 + -18dy + -3dy2 = 0

Solving
7dx + 2dxy + 1dx2 + -18dy + -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), 'd'.
d(7x + 2xy + x2 + -18y + -3y2) = 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 '(7x + 2xy + x2 + -18y + -3y2)' equal to zero and attempt to solve: Simplifying 7x + 2xy + x2 + -18y + -3y2 = 0 Solving 7x + 2xy + x2 + -18y + -3y2 = 0 Move all terms containing d to the left, all other terms to the right. Add '-7x' to each side of the equation. 7x + 2xy + x2 + -18y + -7x + -3y2 = 0 + -7x Reorder the terms: 7x + -7x + 2xy + x2 + -18y + -3y2 = 0 + -7x Combine like terms: 7x + -7x = 0 0 + 2xy + x2 + -18y + -3y2 = 0 + -7x 2xy + x2 + -18y + -3y2 = 0 + -7x Remove the zero: 2xy + x2 + -18y + -3y2 = -7x Add '-2xy' to each side of the equation. 2xy + x2 + -18y + -2xy + -3y2 = -7x + -2xy Reorder the terms: 2xy + -2xy + x2 + -18y + -3y2 = -7x + -2xy Combine like terms: 2xy + -2xy = 0 0 + x2 + -18y + -3y2 = -7x + -2xy x2 + -18y + -3y2 = -7x + -2xy Add '-1x2' to each side of the equation. x2 + -18y + -1x2 + -3y2 = -7x + -2xy + -1x2 Reorder the terms: x2 + -1x2 + -18y + -3y2 = -7x + -2xy + -1x2 Combine like terms: x2 + -1x2 = 0 0 + -18y + -3y2 = -7x + -2xy + -1x2 -18y + -3y2 = -7x + -2xy + -1x2 Add '18y' to each side of the equation. -18y + 18y + -3y2 = -7x + -2xy + -1x2 + 18y Combine like terms: -18y + 18y = 0 0 + -3y2 = -7x + -2xy + -1x2 + 18y -3y2 = -7x + -2xy + -1x2 + 18y Add '3y2' to each side of the equation. -3y2 + 3y2 = -7x + -2xy + -1x2 + 18y + 3y2 Combine like terms: -3y2 + 3y2 = 0 0 = -7x + -2xy + -1x2 + 18y + 3y2 Simplifying 0 = -7x + -2xy + -1x2 + 18y + 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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