(5x+7y)dx-(7x+6y)dy=0

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Solution for (5x+7y)dx-(7x+6y)dy=0 equation: 


Simplifying
(5x + 7y) * dx + -1(7x + 6y) * dy = 0

Reorder the terms for easier multiplication:
dx(5x + 7y) + -1(7x + 6y) * dy = 0
(5x * dx + 7y * dx) + -1(7x + 6y) * dy = 0

Reorder the terms:
(7dxy + 5dx2) + -1(7x + 6y) * dy = 0
(7dxy + 5dx2) + -1(7x + 6y) * dy = 0

Reorder the terms for easier multiplication:
7dxy + 5dx2 + -1dy(7x + 6y) = 0
7dxy + 5dx2 + (7x * -1dy + 6y * -1dy) = 0
7dxy + 5dx2 + (-7dxy + -6dy2) = 0

Reorder the terms:
7dxy + -7dxy + 5dx2 + -6dy2 = 0

Combine like terms: 7dxy + -7dxy = 0
0 + 5dx2 + -6dy2 = 0
5dx2 + -6dy2 = 0

Solving
5dx2 + -6dy2 = 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(5x2 + -6y2) = 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 '(5x2 + -6y2)' equal to zero and attempt to solve:

Simplifying
5x2 + -6y2 = 0

Solving
5x2 + -6y2 = 0

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

Add '-5x2' to each side of the equation.
5x2 + -5x2 + -6y2 = 0 + -5x2

Combine like terms: 5x2 + -5x2 = 0
0 + -6y2 = 0 + -5x2
-6y2 = 0 + -5x2
Remove the zero:
-6y2 = -5x2

Add '6y2' to each side of the equation.
-6y2 + 6y2 = -5x2 + 6y2

Combine like terms: -6y2 + 6y2 = 0
0 = -5x2 + 6y2

Simplifying
0 = -5x2 + 6y2

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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