(2y-3y)dy-(3y-4x)dx=0

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Solution for (2y-3y)dy-(3y-4x)dx=0 equation: 


Simplifying
(2y + -3y) * dy + -1(3y + -4x) * dx = 0

Combine like terms: 2y + -3y = -1y
(-1y) * dy + -1(3y + -4x) * dx = 0

Remove parenthesis around (-1y)
-1y * dy + -1(3y + -4x) * dx = 0

Multiply y * dy
-1dy2 + -1(3y + -4x) * dx = 0

Reorder the terms:
-1dy2 + -1(-4x + 3y) * dx = 0

Reorder the terms for easier multiplication:
-1dy2 + -1dx(-4x + 3y) = 0
-1dy2 + (-4x * -1dx + 3y * -1dx) = 0

Reorder the terms:
-1dy2 + (-3dxy + 4dx2) = 0
-1dy2 + (-3dxy + 4dx2) = 0

Reorder the terms:
-3dxy + 4dx2 + -1dy2 = 0

Solving
-3dxy + 4dx2 + -1dy2 = 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 + 4x2 + -1y2) = 0

Factor a trinomial.
d((x + -1y)(4x + y)) = 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 '(4x + y)' equal to zero and attempt to solve:

Simplifying
4x + y = 0

Solving
4x + y = 0

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

Add '-4x' to each side of the equation.
4x + -4x + y = 0 + -4x

Combine like terms: 4x + -4x = 0
0 + y = 0 + -4x
y = 0 + -4x
Remove the zero:
y = -4x

Add '-1y' to each side of the equation.
y + -1y = -4x + -1y

Combine like terms: y + -1y = 0
0 = -4x + -1y

Simplifying
0 = -4x + -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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