(3y-7x)dx-(3x-7y)dy=0e

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


Simplifying
(3y + -7x) * dx + -1(3x + -7y) * dy = 0e

Reorder the terms:
(-7x + 3y) * dx + -1(3x + -7y) * dy = 0e

Reorder the terms for easier multiplication:
dx(-7x + 3y) + -1(3x + -7y) * dy = 0e
(-7x * dx + 3y * dx) + -1(3x + -7y) * dy = 0e

Reorder the terms:
(3dxy + -7dx2) + -1(3x + -7y) * dy = 0e
(3dxy + -7dx2) + -1(3x + -7y) * dy = 0e

Reorder the terms for easier multiplication:
3dxy + -7dx2 + -1dy(3x + -7y) = 0e
3dxy + -7dx2 + (3x * -1dy + -7y * -1dy) = 0e
3dxy + -7dx2 + (-3dxy + 7dy2) = 0e

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

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

Anything times zero is zero.
-7dx2 + 7dy2 = 0e

Solving
-7dx2 + 7dy2 = 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), '7d'.
7d(-1x2 + y2) = 0

Factor a difference between two squares.
7d((x + y)(-1x + y)) = 0

Ignore the factor 7.

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 '(x + y)' equal to zero and attempt to solve:

Simplifying
x + y = 0

Solving
x + y = 0

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

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

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

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

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

Simplifying
0 = -1x + -1y

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 '(-1x + y)' equal to zero and attempt to solve:

Simplifying
-1x + y = 0

Solving
-1x + y = 0

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

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

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

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

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

Simplifying
0 = x + -1y

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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