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

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


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

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

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

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

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

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

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

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

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

Solving
7dx + -5dxy + 3dx2 + -7dy + 2dy2 = 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 + -5xy + 3x2 + -7y + 2y2) = 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 + -5xy + 3x2 + -7y + 2y2)' equal to zero and attempt to solve:

Simplifying
7x + -5xy + 3x2 + -7y + 2y2 = 0

Solving
7x + -5xy + 3x2 + -7y + 2y2 = 0

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

Add '-7x' to each side of the equation.
7x + -5xy + 3x2 + -7y + -7x + 2y2 = 0 + -7x

Reorder the terms:
7x + -7x + -5xy + 3x2 + -7y + 2y2 = 0 + -7x

Combine like terms: 7x + -7x = 0
0 + -5xy + 3x2 + -7y + 2y2 = 0 + -7x
-5xy + 3x2 + -7y + 2y2 = 0 + -7x
Remove the zero:
-5xy + 3x2 + -7y + 2y2 = -7x

Add '5xy' to each side of the equation.
-5xy + 3x2 + -7y + 5xy + 2y2 = -7x + 5xy

Reorder the terms:
-5xy + 5xy + 3x2 + -7y + 2y2 = -7x + 5xy

Combine like terms: -5xy + 5xy = 0
0 + 3x2 + -7y + 2y2 = -7x + 5xy
3x2 + -7y + 2y2 = -7x + 5xy

Add '-3x2' to each side of the equation.
3x2 + -7y + -3x2 + 2y2 = -7x + 5xy + -3x2

Reorder the terms:
3x2 + -3x2 + -7y + 2y2 = -7x + 5xy + -3x2

Combine like terms: 3x2 + -3x2 = 0
0 + -7y + 2y2 = -7x + 5xy + -3x2
-7y + 2y2 = -7x + 5xy + -3x2

Add '7y' to each side of the equation.
-7y + 7y + 2y2 = -7x + 5xy + -3x2 + 7y

Combine like terms: -7y + 7y = 0
0 + 2y2 = -7x + 5xy + -3x2 + 7y
2y2 = -7x + 5xy + -3x2 + 7y

Add '-2y2' to each side of the equation.
2y2 + -2y2 = -7x + 5xy + -3x2 + 7y + -2y2

Combine like terms: 2y2 + -2y2 = 0
0 = -7x + 5xy + -3x2 + 7y + -2y2

Simplifying
0 = -7x + 5xy + -3x2 + 7y + -2y2

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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