dy(2x-5y)=dx(3x-2y)

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Solution for dy(2x-5y)=dx(3x-2y) equation: 


Simplifying
dy(2x + -5y) = dx(3x + -2y)
(2x * dy + -5y * dy) = dx(3x + -2y)
(2dxy + -5dy2) = dx(3x + -2y)
2dxy + -5dy2 = (3x * dx + -2y * dx)

Reorder the terms:
2dxy + -5dy2 = (-2dxy + 3dx2)
2dxy + -5dy2 = (-2dxy + 3dx2)

Solving
2dxy + -5dy2 = -2dxy + 3dx2

Solving for variable 'd'.

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

Add '2dxy' to each side of the equation.
2dxy + 2dxy + -5dy2 = -2dxy + 2dxy + 3dx2

Combine like terms: 2dxy + 2dxy = 4dxy
4dxy + -5dy2 = -2dxy + 2dxy + 3dx2

Combine like terms: -2dxy + 2dxy = 0
4dxy + -5dy2 = 0 + 3dx2
4dxy + -5dy2 = 3dx2

Add '-3dx2' to each side of the equation.
4dxy + -3dx2 + -5dy2 = 3dx2 + -3dx2

Combine like terms: 3dx2 + -3dx2 = 0
4dxy + -3dx2 + -5dy2 = 0

Factor out the Greatest Common Factor (GCF), 'd'.
d(4xy + -3x2 + -5y2) = 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 '(4xy + -3x2 + -5y2)' equal to zero and attempt to solve:

Simplifying
4xy + -3x2 + -5y2 = 0

Solving
4xy + -3x2 + -5y2 = 0

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

Add '-4xy' to each side of the equation.
4xy + -3x2 + -4xy + -5y2 = 0 + -4xy

Reorder the terms:
4xy + -4xy + -3x2 + -5y2 = 0 + -4xy

Combine like terms: 4xy + -4xy = 0
0 + -3x2 + -5y2 = 0 + -4xy
-3x2 + -5y2 = 0 + -4xy
Remove the zero:
-3x2 + -5y2 = -4xy

Add '3x2' to each side of the equation.
-3x2 + 3x2 + -5y2 = -4xy + 3x2

Combine like terms: -3x2 + 3x2 = 0
0 + -5y2 = -4xy + 3x2
-5y2 = -4xy + 3x2

Add '5y2' to each side of the equation.
-5y2 + 5y2 = -4xy + 3x2 + 5y2

Combine like terms: -5y2 + 5y2 = 0
0 = -4xy + 3x2 + 5y2

Simplifying
0 = -4xy + 3x2 + 5y2

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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