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

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


Simplifying
(x + 2y + -4) * dx + -1(2x + -4y) * dy = 0

Reorder the terms:
(-4 + x + 2y) * dx + -1(2x + -4y) * dy = 0

Reorder the terms for easier multiplication:
dx(-4 + x + 2y) + -1(2x + -4y) * dy = 0
(-4 * dx + x * dx + 2y * dx) + -1(2x + -4y) * dy = 0

Reorder the terms:
(-4dx + 2dxy + dx2) + -1(2x + -4y) * dy = 0
(-4dx + 2dxy + dx2) + -1(2x + -4y) * dy = 0

Reorder the terms for easier multiplication:
-4dx + 2dxy + dx2 + -1dy(2x + -4y) = 0
-4dx + 2dxy + dx2 + (2x * -1dy + -4y * -1dy) = 0
-4dx + 2dxy + dx2 + (-2dxy + 4dy2) = 0

Reorder the terms:
-4dx + 2dxy + -2dxy + dx2 + 4dy2 = 0

Combine like terms: 2dxy + -2dxy = 0
-4dx + 0 + dx2 + 4dy2 = 0
-4dx + dx2 + 4dy2 = 0

Solving
-4dx + dx2 + 4dy2 = 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(-4x + x2 + 4y2) = 0

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

Simplifying
x + -2y = 0

Solving
x + -2y = 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 + -2y = 0 + -1x

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

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

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

Simplifying
0 = -1x + 2y

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 '(x + -2y)' equal to zero and attempt to solve:

Simplifying
x + -2y = 0

Solving
x + -2y = 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 + -2y = 0 + -1x

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

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

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

Simplifying
0 = -1x + 2y

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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