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

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


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

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

Reorder the terms:
elosv((4dxy + 7dx2)) + ((4x + 3y) * dy) = 0
elosv((4dxy + 7dx2)) + ((4x + 3y) * dy) = 0
(4dxy * elosv + 7dx2 * elosv) + ((4x + 3y) * dy) = 0
(4delosvxy + 7delosvx2) + ((4x + 3y) * dy) = 0

Reorder the terms for easier multiplication:
4delosvxy + 7delosvx2 + (dy(4x + 3y)) = 0
4delosvxy + 7delosvx2 + ((4x * dy + 3y * dy)) = 0
4delosvxy + 7delosvx2 + ((4dxy + 3dy2)) = 0
4delosvxy + 7delosvx2 + (4dxy + 3dy2) = 0

Remove parenthesis around (4dxy + 3dy2)
4delosvxy + 7delosvx2 + 4dxy + 3dy2 = 0

Solving
4delosvxy + 7delosvx2 + 4dxy + 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(4elosvxy + 7elosvx2 + 4xy + 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 '(4elosvxy + 7elosvx2 + 4xy + 3y2)' equal to zero and attempt to solve:

Simplifying
4elosvxy + 7elosvx2 + 4xy + 3y2 = 0

Solving
4elosvxy + 7elosvx2 + 4xy + 3y2 = 0

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

Add '-4elosvxy' to each side of the equation.
4elosvxy + 7elosvx2 + 4xy + -4elosvxy + 3y2 = 0 + -4elosvxy

Reorder the terms:
4elosvxy + -4elosvxy + 7elosvx2 + 4xy + 3y2 = 0 + -4elosvxy

Combine like terms: 4elosvxy + -4elosvxy = 0
0 + 7elosvx2 + 4xy + 3y2 = 0 + -4elosvxy
7elosvx2 + 4xy + 3y2 = 0 + -4elosvxy
Remove the zero:
7elosvx2 + 4xy + 3y2 = -4elosvxy

Add '-7elosvx2' to each side of the equation.
7elosvx2 + 4xy + -7elosvx2 + 3y2 = -4elosvxy + -7elosvx2

Reorder the terms:
7elosvx2 + -7elosvx2 + 4xy + 3y2 = -4elosvxy + -7elosvx2

Combine like terms: 7elosvx2 + -7elosvx2 = 0
0 + 4xy + 3y2 = -4elosvxy + -7elosvx2
4xy + 3y2 = -4elosvxy + -7elosvx2

Add '-4xy' to each side of the equation.
4xy + -4xy + 3y2 = -4elosvxy + -7elosvx2 + -4xy

Combine like terms: 4xy + -4xy = 0
0 + 3y2 = -4elosvxy + -7elosvx2 + -4xy
3y2 = -4elosvxy + -7elosvx2 + -4xy

Add '-3y2' to each side of the equation.
3y2 + -3y2 = -4elosvxy + -7elosvx2 + -4xy + -3y2

Combine like terms: 3y2 + -3y2 = 0
0 = -4elosvxy + -7elosvx2 + -4xy + -3y2

Simplifying
0 = -4elosvxy + -7elosvx2 + -4xy + -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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