(5x-2y+7)dy+(4x-3y+8)dx=

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Solution for (5x-2y+7)dy+(4x-3y+8)dx= equation: 


Simplifying
(5x + -2y + 7) * dy + (4x + -3y + 8) * dx = 0

Reorder the terms:
(7 + 5x + -2y) * dy + (4x + -3y + 8) * dx = 0

Reorder the terms for easier multiplication:
dy(7 + 5x + -2y) + (4x + -3y + 8) * dx = 0
(7 * dy + 5x * dy + -2y * dy) + (4x + -3y + 8) * dx = 0

Reorder the terms:
(5dxy + 7dy + -2dy2) + (4x + -3y + 8) * dx = 0
(5dxy + 7dy + -2dy2) + (4x + -3y + 8) * dx = 0

Reorder the terms:
5dxy + 7dy + -2dy2 + (8 + 4x + -3y) * dx = 0

Reorder the terms for easier multiplication:
5dxy + 7dy + -2dy2 + dx(8 + 4x + -3y) = 0
5dxy + 7dy + -2dy2 + (8 * dx + 4x * dx + -3y * dx) = 0

Reorder the terms:
5dxy + 7dy + -2dy2 + (8dx + -3dxy + 4dx2) = 0
5dxy + 7dy + -2dy2 + (8dx + -3dxy + 4dx2) = 0

Reorder the terms:
8dx + 5dxy + -3dxy + 4dx2 + 7dy + -2dy2 = 0

Combine like terms: 5dxy + -3dxy = 2dxy
8dx + 2dxy + 4dx2 + 7dy + -2dy2 = 0

Solving
8dx + 2dxy + 4dx2 + 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(8x + 2xy + 4x2 + 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 '(8x + 2xy + 4x2 + 7y + -2y2)' equal to zero and attempt to solve:

Simplifying
8x + 2xy + 4x2 + 7y + -2y2 = 0

Solving
8x + 2xy + 4x2 + 7y + -2y2 = 0

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

Add '-8x' to each side of the equation.
8x + 2xy + 4x2 + 7y + -8x + -2y2 = 0 + -8x

Reorder the terms:
8x + -8x + 2xy + 4x2 + 7y + -2y2 = 0 + -8x

Combine like terms: 8x + -8x = 0
0 + 2xy + 4x2 + 7y + -2y2 = 0 + -8x
2xy + 4x2 + 7y + -2y2 = 0 + -8x
Remove the zero:
2xy + 4x2 + 7y + -2y2 = -8x

Add '-2xy' to each side of the equation.
2xy + 4x2 + 7y + -2xy + -2y2 = -8x + -2xy

Reorder the terms:
2xy + -2xy + 4x2 + 7y + -2y2 = -8x + -2xy

Combine like terms: 2xy + -2xy = 0
0 + 4x2 + 7y + -2y2 = -8x + -2xy
4x2 + 7y + -2y2 = -8x + -2xy

Add '-4x2' to each side of the equation.
4x2 + 7y + -4x2 + -2y2 = -8x + -2xy + -4x2

Reorder the terms:
4x2 + -4x2 + 7y + -2y2 = -8x + -2xy + -4x2

Combine like terms: 4x2 + -4x2 = 0
0 + 7y + -2y2 = -8x + -2xy + -4x2
7y + -2y2 = -8x + -2xy + -4x2

Add '-7y' to each side of the equation.
7y + -7y + -2y2 = -8x + -2xy + -4x2 + -7y

Combine like terms: 7y + -7y = 0
0 + -2y2 = -8x + -2xy + -4x2 + -7y
-2y2 = -8x + -2xy + -4x2 + -7y

Add '2y2' to each side of the equation.
-2y2 + 2y2 = -8x + -2xy + -4x2 + -7y + 2y2

Combine like terms: -2y2 + 2y2 = 0
0 = -8x + -2xy + -4x2 + -7y + 2y2

Simplifying
0 = -8x + -2xy + -4x2 + -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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