(7x-3y+2)dx+(5y-3x+5)dy=0

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Solution for (7x-3y+2)dx+(5y-3x+5)dy=0 equation: 


Simplifying
(7x + -3y + 2) * dx + (5y + -3x + 5) * dy = 0

Reorder the terms:
(2 + 7x + -3y) * dx + (5y + -3x + 5) * dy = 0

Reorder the terms for easier multiplication:
dx(2 + 7x + -3y) + (5y + -3x + 5) * dy = 0
(2 * dx + 7x * dx + -3y * dx) + (5y + -3x + 5) * dy = 0

Reorder the terms:
(2dx + -3dxy + 7dx2) + (5y + -3x + 5) * dy = 0
(2dx + -3dxy + 7dx2) + (5y + -3x + 5) * dy = 0

Reorder the terms:
2dx + -3dxy + 7dx2 + (5 + -3x + 5y) * dy = 0

Reorder the terms for easier multiplication:
2dx + -3dxy + 7dx2 + dy(5 + -3x + 5y) = 0
2dx + -3dxy + 7dx2 + (5 * dy + -3x * dy + 5y * dy) = 0

Reorder the terms:
2dx + -3dxy + 7dx2 + (-3dxy + 5dy + 5dy2) = 0
2dx + -3dxy + 7dx2 + (-3dxy + 5dy + 5dy2) = 0

Reorder the terms:
2dx + -3dxy + -3dxy + 7dx2 + 5dy + 5dy2 = 0

Combine like terms: -3dxy + -3dxy = -6dxy
2dx + -6dxy + 7dx2 + 5dy + 5dy2 = 0

Solving
2dx + -6dxy + 7dx2 + 5dy + 5dy2 = 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(2x + -6xy + 7x2 + 5y + 5y2) = 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 '(2x + -6xy + 7x2 + 5y + 5y2)' equal to zero and attempt to solve:

Simplifying
2x + -6xy + 7x2 + 5y + 5y2 = 0

Solving
2x + -6xy + 7x2 + 5y + 5y2 = 0

Move all terms containing d to the left, all other terms to the right.

Add '-2x' to each side of the equation.
2x + -6xy + 7x2 + 5y + -2x + 5y2 = 0 + -2x

Reorder the terms:
2x + -2x + -6xy + 7x2 + 5y + 5y2 = 0 + -2x

Combine like terms: 2x + -2x = 0
0 + -6xy + 7x2 + 5y + 5y2 = 0 + -2x
-6xy + 7x2 + 5y + 5y2 = 0 + -2x
Remove the zero:
-6xy + 7x2 + 5y + 5y2 = -2x

Add '6xy' to each side of the equation.
-6xy + 7x2 + 5y + 6xy + 5y2 = -2x + 6xy

Reorder the terms:
-6xy + 6xy + 7x2 + 5y + 5y2 = -2x + 6xy

Combine like terms: -6xy + 6xy = 0
0 + 7x2 + 5y + 5y2 = -2x + 6xy
7x2 + 5y + 5y2 = -2x + 6xy

Add '-7x2' to each side of the equation.
7x2 + 5y + -7x2 + 5y2 = -2x + 6xy + -7x2

Reorder the terms:
7x2 + -7x2 + 5y + 5y2 = -2x + 6xy + -7x2

Combine like terms: 7x2 + -7x2 = 0
0 + 5y + 5y2 = -2x + 6xy + -7x2
5y + 5y2 = -2x + 6xy + -7x2

Add '-5y' to each side of the equation.
5y + -5y + 5y2 = -2x + 6xy + -7x2 + -5y

Combine like terms: 5y + -5y = 0
0 + 5y2 = -2x + 6xy + -7x2 + -5y
5y2 = -2x + 6xy + -7x2 + -5y

Add '-5y2' to each side of the equation.
5y2 + -5y2 = -2x + 6xy + -7x2 + -5y + -5y2

Combine like terms: 5y2 + -5y2 = 0
0 = -2x + 6xy + -7x2 + -5y + -5y2

Simplifying
0 = -2x + 6xy + -7x2 + -5y + -5y2

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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