(8y-6x)dx+(y-7x)dy=0

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Solution for (8y-6x)dx+(y-7x)dy=0 equation: 


Simplifying
(8y + -6x) * dx + (y + -7x) * dy = 0

Reorder the terms:
(-6x + 8y) * dx + (y + -7x) * dy = 0

Reorder the terms for easier multiplication:
dx(-6x + 8y) + (y + -7x) * dy = 0
(-6x * dx + 8y * dx) + (y + -7x) * dy = 0

Reorder the terms:
(8dxy + -6dx2) + (y + -7x) * dy = 0
(8dxy + -6dx2) + (y + -7x) * dy = 0

Reorder the terms:
8dxy + -6dx2 + (-7x + y) * dy = 0

Reorder the terms for easier multiplication:
8dxy + -6dx2 + dy(-7x + y) = 0
8dxy + -6dx2 + (-7x * dy + y * dy) = 0
8dxy + -6dx2 + (-7dxy + dy2) = 0

Reorder the terms:
8dxy + -7dxy + -6dx2 + dy2 = 0

Combine like terms: 8dxy + -7dxy = 1dxy
1dxy + -6dx2 + dy2 = 0

Solving
1dxy + -6dx2 + dy2 = 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(xy + -6x2 + y2) = 0

Factor a trinomial.
d((-3x + -1y)(2x + -1y)) = 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 '(-3x + -1y)' equal to zero and attempt to solve:

Simplifying
-3x + -1y = 0

Solving
-3x + -1y = 0

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

Add '3x' to each side of the equation.
-3x + 3x + -1y = 0 + 3x

Combine like terms: -3x + 3x = 0
0 + -1y = 0 + 3x
-1y = 0 + 3x
Remove the zero:
-1y = 3x

Add 'y' to each side of the equation.
-1y + y = 3x + y

Combine like terms: -1y + y = 0
0 = 3x + y

Simplifying
0 = 3x + y

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 3
Set the factor '(2x + -1y)' equal to zero and attempt to solve:

Simplifying
2x + -1y = 0

Solving
2x + -1y = 0

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

Add '-2x' to each side of the equation.
2x + -2x + -1y = 0 + -2x

Combine like terms: 2x + -2x = 0
0 + -1y = 0 + -2x
-1y = 0 + -2x
Remove the zero:
-1y = -2x

Add 'y' to each side of the equation.
-1y + y = -2x + y

Combine like terms: -1y + y = 0
0 = -2x + y

Simplifying
0 = -2x + y

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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