(X-4y)*dx+(x-2y)*dy=0

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Solution for (X-4y)*dx+(x-2y)*dy=0 equation: 


Simplifying
(X + -4y) * dx + (x + -2y) * dy = 0

Reorder the terms for easier multiplication:
dx(X + -4y) + (x + -2y) * dy = 0
(X * dx + -4y * dx) + (x + -2y) * dy = 0
(dxX + -4dxy) + (x + -2y) * dy = 0

Reorder the terms for easier multiplication:
dxX + -4dxy + dy(x + -2y) = 0
dxX + -4dxy + (x * dy + -2y * dy) = 0
dxX + -4dxy + (dxy + -2dy2) = 0

Combine like terms: -4dxy + dxy = -3dxy
dxX + -3dxy + -2dy2 = 0

Solving
dxX + -3dxy + -2dy2 = 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(xX + -3xy + -2y2) = 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 '(xX + -3xy + -2y2)' equal to zero and attempt to solve:

Simplifying
xX + -3xy + -2y2 = 0

Solving
xX + -3xy + -2y2 = 0

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

Add '-1xX' to each side of the equation.
xX + -3xy + -1xX + -2y2 = 0 + -1xX

Reorder the terms:
xX + -1xX + -3xy + -2y2 = 0 + -1xX

Combine like terms: xX + -1xX = 0
0 + -3xy + -2y2 = 0 + -1xX
-3xy + -2y2 = 0 + -1xX
Remove the zero:
-3xy + -2y2 = -1xX

Add '3xy' to each side of the equation.
-3xy + 3xy + -2y2 = -1xX + 3xy

Combine like terms: -3xy + 3xy = 0
0 + -2y2 = -1xX + 3xy
-2y2 = -1xX + 3xy

Add '2y2' to each side of the equation.
-2y2 + 2y2 = -1xX + 3xy + 2y2

Combine like terms: -2y2 + 2y2 = 0
0 = -1xX + 3xy + 2y2

Simplifying
0 = -1xX + 3xy + 2y2

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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