(3y-7x+7)dx-(3x-7y-3)dy=0

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Solution for (3y-7x+7)dx-(3x-7y-3)dy=0 equation:


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

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

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

Reorder the terms:
(7dx + 3dxy + -7dx2) + -1(3x + -7y + -3) * dy = 0
(7dx + 3dxy + -7dx2) + -1(3x + -7y + -3) * dy = 0

Reorder the terms:
7dx + 3dxy + -7dx2 + -1(-3 + 3x + -7y) * dy = 0

Reorder the terms for easier multiplication:
7dx + 3dxy + -7dx2 + -1dy(-3 + 3x + -7y) = 0
7dx + 3dxy + -7dx2 + (-3 * -1dy + 3x * -1dy + -7y * -1dy) = 0

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

Reorder the terms:
7dx + 3dxy + -3dxy + -7dx2 + 3dy + 7dy2 = 0

Combine like terms: 3dxy + -3dxy = 0
7dx + 0 + -7dx2 + 3dy + 7dy2 = 0
7dx + -7dx2 + 3dy + 7dy2 = 0

Solving
7dx + -7dx2 + 3dy + 7dy2 = 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 + -7x2 + 3y + 7y2) = 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 + -7x2 + 3y + 7y2)' equal to zero and attempt to solve: Simplifying 7x + -7x2 + 3y + 7y2 = 0 Solving 7x + -7x2 + 3y + 7y2 = 0 Move all terms containing d to the left, all other terms to the right. Add '-7x' to each side of the equation. 7x + -7x2 + 3y + -7x + 7y2 = 0 + -7x Reorder the terms: 7x + -7x + -7x2 + 3y + 7y2 = 0 + -7x Combine like terms: 7x + -7x = 0 0 + -7x2 + 3y + 7y2 = 0 + -7x -7x2 + 3y + 7y2 = 0 + -7x Remove the zero: -7x2 + 3y + 7y2 = -7x Add '7x2' to each side of the equation. -7x2 + 3y + 7x2 + 7y2 = -7x + 7x2 Reorder the terms: -7x2 + 7x2 + 3y + 7y2 = -7x + 7x2 Combine like terms: -7x2 + 7x2 = 0 0 + 3y + 7y2 = -7x + 7x2 3y + 7y2 = -7x + 7x2 Add '-3y' to each side of the equation. 3y + -3y + 7y2 = -7x + 7x2 + -3y Combine like terms: 3y + -3y = 0 0 + 7y2 = -7x + 7x2 + -3y 7y2 = -7x + 7x2 + -3y Add '-7y2' to each side of the equation. 7y2 + -7y2 = -7x + 7x2 + -3y + -7y2 Combine like terms: 7y2 + -7y2 = 0 0 = -7x + 7x2 + -3y + -7y2 Simplifying 0 = -7x + 7x2 + -3y + -7y2 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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