(2x-3y)*dx+y*dy=0

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Solution for (2x-3y)*dx+y*dy=0 equation: 


Simplifying
(2x + -3y) * dx + y * dy = 0

Reorder the terms for easier multiplication:
dx(2x + -3y) + y * dy = 0
(2x * dx + -3y * dx) + y * dy = 0

Reorder the terms:
(-3dxy + 2dx2) + y * dy = 0
(-3dxy + 2dx2) + y * dy = 0

Multiply y * dy
-3dxy + 2dx2 + dy2 = 0

Solving
-3dxy + 2dx2 + 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(-3xy + 2x2 + y2) = 0

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

Simplifying
x + -1y = 0

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

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

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

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

Simplifying
0 = -1x + 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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