(3x-2y+4)dx-(2x+7y-1)dy=0

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Solution for (3x-2y+4)dx-(2x+7y-1)dy=0 equation: 


Simplifying
(3x + -2y + 4) * dx + -1(2x + 7y + -1) * dy = 0

Reorder the terms:
(4 + 3x + -2y) * dx + -1(2x + 7y + -1) * dy = 0

Reorder the terms for easier multiplication:
dx(4 + 3x + -2y) + -1(2x + 7y + -1) * dy = 0
(4 * dx + 3x * dx + -2y * dx) + -1(2x + 7y + -1) * dy = 0

Reorder the terms:
(4dx + -2dxy + 3dx2) + -1(2x + 7y + -1) * dy = 0
(4dx + -2dxy + 3dx2) + -1(2x + 7y + -1) * dy = 0

Reorder the terms:
4dx + -2dxy + 3dx2 + -1(-1 + 2x + 7y) * dy = 0

Reorder the terms for easier multiplication:
4dx + -2dxy + 3dx2 + -1dy(-1 + 2x + 7y) = 0
4dx + -2dxy + 3dx2 + (-1 * -1dy + 2x * -1dy + 7y * -1dy) = 0

Reorder the terms:
4dx + -2dxy + 3dx2 + (-2dxy + 1dy + -7dy2) = 0
4dx + -2dxy + 3dx2 + (-2dxy + 1dy + -7dy2) = 0

Reorder the terms:
4dx + -2dxy + -2dxy + 3dx2 + 1dy + -7dy2 = 0

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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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