(7x-3y)dx+(6y-3x)dy=0

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Solution for (7x-3y)dx+(6y-3x)dy=0 equation: 


Simplifying
(7x + -3y) * dx + (6y + -3x) * dy = 0

Reorder the terms for easier multiplication:
dx(7x + -3y) + (6y + -3x) * dy = 0
(7x * dx + -3y * dx) + (6y + -3x) * dy = 0

Reorder the terms:
(-3dxy + 7dx2) + (6y + -3x) * dy = 0
(-3dxy + 7dx2) + (6y + -3x) * dy = 0

Reorder the terms:
-3dxy + 7dx2 + (-3x + 6y) * dy = 0

Reorder the terms for easier multiplication:
-3dxy + 7dx2 + dy(-3x + 6y) = 0
-3dxy + 7dx2 + (-3x * dy + 6y * dy) = 0
-3dxy + 7dx2 + (-3dxy + 6dy2) = 0

Reorder the terms:
-3dxy + -3dxy + 7dx2 + 6dy2 = 0

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

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

Simplifying
-6xy + 7x2 + 6y2 = 0

Solving
-6xy + 7x2 + 6y2 = 0

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

Add '6xy' to each side of the equation.
-6xy + 7x2 + 6xy + 6y2 = 0 + 6xy

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

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

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

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

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

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

Simplifying
0 = 6xy + -7x2 + -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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