(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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