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

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


Simplifying
(3x + 2y + 7) * dx + (2x + -1y) * dy = 0

Reorder the terms:
(7 + 3x + 2y) * dx + (2x + -1y) * dy = 0

Reorder the terms for easier multiplication:
dx(7 + 3x + 2y) + (2x + -1y) * dy = 0
(7 * dx + 3x * dx + 2y * dx) + (2x + -1y) * dy = 0

Reorder the terms:
(7dx + 2dxy + 3dx2) + (2x + -1y) * dy = 0
(7dx + 2dxy + 3dx2) + (2x + -1y) * dy = 0

Reorder the terms for easier multiplication:
7dx + 2dxy + 3dx2 + dy(2x + -1y) = 0
7dx + 2dxy + 3dx2 + (2x * dy + -1y * dy) = 0
7dx + 2dxy + 3dx2 + (2dxy + -1dy2) = 0

Reorder the terms:
7dx + 2dxy + 2dxy + 3dx2 + -1dy2 = 0

Combine like terms: 2dxy + 2dxy = 4dxy
7dx + 4dxy + 3dx2 + -1dy2 = 0

Solving
7dx + 4dxy + 3dx2 + -1dy2 = 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 + 4xy + 3x2 + -1y2) = 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 + 4xy + 3x2 + -1y2)' equal to zero and attempt to solve:

Simplifying
7x + 4xy + 3x2 + -1y2 = 0

Solving
7x + 4xy + 3x2 + -1y2 = 0

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

Add '-7x' to each side of the equation.
7x + 4xy + 3x2 + -7x + -1y2 = 0 + -7x

Reorder the terms:
7x + -7x + 4xy + 3x2 + -1y2 = 0 + -7x

Combine like terms: 7x + -7x = 0
0 + 4xy + 3x2 + -1y2 = 0 + -7x
4xy + 3x2 + -1y2 = 0 + -7x
Remove the zero:
4xy + 3x2 + -1y2 = -7x

Add '-4xy' to each side of the equation.
4xy + 3x2 + -4xy + -1y2 = -7x + -4xy

Reorder the terms:
4xy + -4xy + 3x2 + -1y2 = -7x + -4xy

Combine like terms: 4xy + -4xy = 0
0 + 3x2 + -1y2 = -7x + -4xy
3x2 + -1y2 = -7x + -4xy

Add '-3x2' to each side of the equation.
3x2 + -3x2 + -1y2 = -7x + -4xy + -3x2

Combine like terms: 3x2 + -3x2 = 0
0 + -1y2 = -7x + -4xy + -3x2
-1y2 = -7x + -4xy + -3x2

Add 'y2' to each side of the equation.
-1y2 + y2 = -7x + -4xy + -3x2 + y2

Combine like terms: -1y2 + y2 = 0
0 = -7x + -4xy + -3x2 + y2

Simplifying
0 = -7x + -4xy + -3x2 + y2

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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