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

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


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

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

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

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

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

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

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

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

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

Solving
-7dx + 6dxy + 4dx2 + 4dy + -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(-7x + 6xy + 4x2 + 4y + -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 '(-7x + 6xy + 4x2 + 4y + -7y2)' equal to zero and attempt to solve:

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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