(2x-3y)dx+(2y-3x)dy=12xy

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Solution for (2x-3y)dx+(2y-3x)dy=12xy equation: 


Simplifying
(2x + -3y) * dx + (2y + -3x) * dy = 12xy

Reorder the terms for easier multiplication:
dx(2x + -3y) + (2y + -3x) * dy = 12xy
(2x * dx + -3y * dx) + (2y + -3x) * dy = 12xy

Reorder the terms:
(-3dxy + 2dx2) + (2y + -3x) * dy = 12xy
(-3dxy + 2dx2) + (2y + -3x) * dy = 12xy

Reorder the terms:
-3dxy + 2dx2 + (-3x + 2y) * dy = 12xy

Reorder the terms for easier multiplication:
-3dxy + 2dx2 + dy(-3x + 2y) = 12xy
-3dxy + 2dx2 + (-3x * dy + 2y * dy) = 12xy
-3dxy + 2dx2 + (-3dxy + 2dy2) = 12xy

Reorder the terms:
-3dxy + -3dxy + 2dx2 + 2dy2 = 12xy

Combine like terms: -3dxy + -3dxy = -6dxy
-6dxy + 2dx2 + 2dy2 = 12xy

Solving
-6dxy + 2dx2 + 2dy2 = 12xy

Solving for variable 'd'.

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

Combine like terms: 12xy + -12xy = 0
-6dxy + 2dx2 + 2dy2 + -12xy = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-3dxy + dx2 + dy2 + -6xy) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-3dxy + dx2 + dy2 + -6xy)' equal to zero and attempt to solve:

Simplifying
-3dxy + dx2 + dy2 + -6xy = 0

Solving
-3dxy + dx2 + dy2 + -6xy = 0

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

Add '6xy' to each side of the equation.
-3dxy + dx2 + dy2 + -6xy + 6xy = 0 + 6xy

Combine like terms: -6xy + 6xy = 0
-3dxy + dx2 + dy2 + 0 = 0 + 6xy
-3dxy + dx2 + dy2 = 0 + 6xy
Remove the zero:
-3dxy + dx2 + dy2 = 6xy

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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