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

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


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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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