(x-2y+7)dx+(2x+7y-2)dy=0

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Solution for (x-2y+7)dx+(2x+7y-2)dy=0 equation: 


Simplifying
(x + -2y + 7) * dx + (2x + 7y + -2) * dy = 0

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

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

Reorder the terms:
(7dx + -2dxy + dx2) + (2x + 7y + -2) * dy = 0
(7dx + -2dxy + dx2) + (2x + 7y + -2) * dy = 0

Reorder the terms:
7dx + -2dxy + dx2 + (-2 + 2x + 7y) * dy = 0

Reorder the terms for easier multiplication:
7dx + -2dxy + dx2 + dy(-2 + 2x + 7y) = 0
7dx + -2dxy + dx2 + (-2 * dy + 2x * dy + 7y * dy) = 0

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

Reorder the terms:
7dx + -2dxy + 2dxy + dx2 + -2dy + 7dy2 = 0

Combine like terms: -2dxy + 2dxy = 0
7dx + 0 + dx2 + -2dy + 7dy2 = 0
7dx + dx2 + -2dy + 7dy2 = 0

Solving
7dx + dx2 + -2dy + 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 + x2 + -2y + 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 + x2 + -2y + 7y2)' equal to zero and attempt to solve:

Simplifying
7x + x2 + -2y + 7y2 = 0

Solving
7x + x2 + -2y + 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 + x2 + -2y + -7x + 7y2 = 0 + -7x

Reorder the terms:
7x + -7x + x2 + -2y + 7y2 = 0 + -7x

Combine like terms: 7x + -7x = 0
0 + x2 + -2y + 7y2 = 0 + -7x
x2 + -2y + 7y2 = 0 + -7x
Remove the zero:
x2 + -2y + 7y2 = -7x

Add '-1x2' to each side of the equation.
x2 + -2y + -1x2 + 7y2 = -7x + -1x2

Reorder the terms:
x2 + -1x2 + -2y + 7y2 = -7x + -1x2

Combine like terms: x2 + -1x2 = 0
0 + -2y + 7y2 = -7x + -1x2
-2y + 7y2 = -7x + -1x2

Add '2y' to each side of the equation.
-2y + 2y + 7y2 = -7x + -1x2 + 2y

Combine like terms: -2y + 2y = 0
0 + 7y2 = -7x + -1x2 + 2y
7y2 = -7x + -1x2 + 2y

Add '-7y2' to each side of the equation.
7y2 + -7y2 = -7x + -1x2 + 2y + -7y2

Combine like terms: 7y2 + -7y2 = 0
0 = -7x + -1x2 + 2y + -7y2

Simplifying
0 = -7x + -1x2 + 2y + -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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