(3y^2+2)dx=(5-6xy)dy

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Solution for (3y^2+2)dx=(5-6xy)dy equation: 


Simplifying
(3y2 + 2) * dx = (5 + -6xy) * dy

Reorder the terms:
(2 + 3y2) * dx = (5 + -6xy) * dy

Reorder the terms for easier multiplication:
dx(2 + 3y2) = (5 + -6xy) * dy
(2 * dx + 3y2 * dx) = (5 + -6xy) * dy
(2dx + 3dxy2) = (5 + -6xy) * dy

Reorder the terms for easier multiplication:
2dx + 3dxy2 = dy(5 + -6xy)
2dx + 3dxy2 = (5 * dy + -6xy * dy)

Reorder the terms:
2dx + 3dxy2 = (-6dxy2 + 5dy)
2dx + 3dxy2 = (-6dxy2 + 5dy)

Solving
2dx + 3dxy2 = -6dxy2 + 5dy

Solving for variable 'd'.

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

Add '6dxy2' to each side of the equation.
2dx + 3dxy2 + 6dxy2 = -6dxy2 + 6dxy2 + 5dy

Combine like terms: 3dxy2 + 6dxy2 = 9dxy2
2dx + 9dxy2 = -6dxy2 + 6dxy2 + 5dy

Combine like terms: -6dxy2 + 6dxy2 = 0
2dx + 9dxy2 = 0 + 5dy
2dx + 9dxy2 = 5dy

Add '-5dy' to each side of the equation.
2dx + 9dxy2 + -5dy = 5dy + -5dy

Combine like terms: 5dy + -5dy = 0
2dx + 9dxy2 + -5dy = 0

Factor out the Greatest Common Factor (GCF), 'd'.
d(2x + 9xy2 + -5y) = 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 '(2x + 9xy2 + -5y)' equal to zero and attempt to solve:

Simplifying
2x + 9xy2 + -5y = 0

Solving
2x + 9xy2 + -5y = 0

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

Add '-2x' to each side of the equation.
2x + 9xy2 + -2x + -5y = 0 + -2x

Reorder the terms:
2x + -2x + 9xy2 + -5y = 0 + -2x

Combine like terms: 2x + -2x = 0
0 + 9xy2 + -5y = 0 + -2x
9xy2 + -5y = 0 + -2x
Remove the zero:
9xy2 + -5y = -2x

Add '-9xy2' to each side of the equation.
9xy2 + -9xy2 + -5y = -2x + -9xy2

Combine like terms: 9xy2 + -9xy2 = 0
0 + -5y = -2x + -9xy2
-5y = -2x + -9xy2

Add '5y' to each side of the equation.
-5y + 5y = -2x + -9xy2 + 5y

Combine like terms: -5y + 5y = 0
0 = -2x + -9xy2 + 5y

Simplifying
0 = -2x + -9xy2 + 5y

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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