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

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


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

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

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

Reorder the terms for easier multiplication:
4dxy + 7dx2 + dy(4x + 3y) = 0
4dxy + 7dx2 + (4x * dy + 3y * dy) = 0
4dxy + 7dx2 + (4dxy + 3dy2) = 0

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

Combine like terms: 4dxy + 4dxy = 8dxy
8dxy + 7dx2 + 3dy2 = 0

Solving
8dxy + 7dx2 + 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(8xy + 7x2 + 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 '(8xy + 7x2 + 3y2)' equal to zero and attempt to solve:

Simplifying
8xy + 7x2 + 3y2 = 0

Solving
8xy + 7x2 + 3y2 = 0

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

Add '-8xy' to each side of the equation.
8xy + 7x2 + -8xy + 3y2 = 0 + -8xy

Reorder the terms:
8xy + -8xy + 7x2 + 3y2 = 0 + -8xy

Combine like terms: 8xy + -8xy = 0
0 + 7x2 + 3y2 = 0 + -8xy
7x2 + 3y2 = 0 + -8xy
Remove the zero:
7x2 + 3y2 = -8xy

Add '-7x2' to each side of the equation.
7x2 + -7x2 + 3y2 = -8xy + -7x2

Combine like terms: 7x2 + -7x2 = 0
0 + 3y2 = -8xy + -7x2
3y2 = -8xy + -7x2

Add '-3y2' to each side of the equation.
3y2 + -3y2 = -8xy + -7x2 + -3y2

Combine like terms: 3y2 + -3y2 = 0
0 = -8xy + -7x2 + -3y2

Simplifying
0 = -8xy + -7x2 + -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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