(2x-3y+2)dy+(4x+4y+7)dx=0

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Solution for (2x-3y+2)dy+(4x+4y+7)dx=0 equation: 


Simplifying
(2x + -3y + 2) * dy + (4x + 4y + 7) * dx = 0

Reorder the terms:
(2 + 2x + -3y) * dy + (4x + 4y + 7) * dx = 0

Reorder the terms for easier multiplication:
dy(2 + 2x + -3y) + (4x + 4y + 7) * dx = 0
(2 * dy + 2x * dy + -3y * dy) + (4x + 4y + 7) * dx = 0

Reorder the terms:
(2dxy + 2dy + -3dy2) + (4x + 4y + 7) * dx = 0
(2dxy + 2dy + -3dy2) + (4x + 4y + 7) * dx = 0

Reorder the terms:
2dxy + 2dy + -3dy2 + (7 + 4x + 4y) * dx = 0

Reorder the terms for easier multiplication:
2dxy + 2dy + -3dy2 + dx(7 + 4x + 4y) = 0
2dxy + 2dy + -3dy2 + (7 * dx + 4x * dx + 4y * dx) = 0

Reorder the terms:
2dxy + 2dy + -3dy2 + (7dx + 4dxy + 4dx2) = 0
2dxy + 2dy + -3dy2 + (7dx + 4dxy + 4dx2) = 0

Reorder the terms:
7dx + 2dxy + 4dxy + 4dx2 + 2dy + -3dy2 = 0

Combine like terms: 2dxy + 4dxy = 6dxy
7dx + 6dxy + 4dx2 + 2dy + -3dy2 = 0

Solving
7dx + 6dxy + 4dx2 + 2dy + -3dy2 = 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 + 4x2 + 2y + -3y2) = 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 + 4x2 + 2y + -3y2)' equal to zero and attempt to solve:

Simplifying
7x + 6xy + 4x2 + 2y + -3y2 = 0

Solving
7x + 6xy + 4x2 + 2y + -3y2 = 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 + 4x2 + 2y + -7x + -3y2 = 0 + -7x

Reorder the terms:
7x + -7x + 6xy + 4x2 + 2y + -3y2 = 0 + -7x

Combine like terms: 7x + -7x = 0
0 + 6xy + 4x2 + 2y + -3y2 = 0 + -7x
6xy + 4x2 + 2y + -3y2 = 0 + -7x
Remove the zero:
6xy + 4x2 + 2y + -3y2 = -7x

Add '-6xy' to each side of the equation.
6xy + 4x2 + 2y + -6xy + -3y2 = -7x + -6xy

Reorder the terms:
6xy + -6xy + 4x2 + 2y + -3y2 = -7x + -6xy

Combine like terms: 6xy + -6xy = 0
0 + 4x2 + 2y + -3y2 = -7x + -6xy
4x2 + 2y + -3y2 = -7x + -6xy

Add '-4x2' to each side of the equation.
4x2 + 2y + -4x2 + -3y2 = -7x + -6xy + -4x2

Reorder the terms:
4x2 + -4x2 + 2y + -3y2 = -7x + -6xy + -4x2

Combine like terms: 4x2 + -4x2 = 0
0 + 2y + -3y2 = -7x + -6xy + -4x2
2y + -3y2 = -7x + -6xy + -4x2

Add '-2y' to each side of the equation.
2y + -2y + -3y2 = -7x + -6xy + -4x2 + -2y

Combine like terms: 2y + -2y = 0
0 + -3y2 = -7x + -6xy + -4x2 + -2y
-3y2 = -7x + -6xy + -4x2 + -2y

Add '3y2' to each side of the equation.
-3y2 + 3y2 = -7x + -6xy + -4x2 + -2y + 3y2

Combine like terms: -3y2 + 3y2 = 0
0 = -7x + -6xy + -4x2 + -2y + 3y2

Simplifying
0 = -7x + -6xy + -4x2 + -2y + 3y2

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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