dx(3x^2+2y^2)=dy(4xy+6y^2)

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Solution for dx(3x^2+2y^2)=dy(4xy+6y^2) equation: 


Simplifying
dx(3x2 + 2y2) = dy(4xy + 6y2)
(3x2 * dx + 2y2 * dx) = dy(4xy + 6y2)

Reorder the terms:
(2dxy2 + 3dx3) = dy(4xy + 6y2)
(2dxy2 + 3dx3) = dy(4xy + 6y2)
2dxy2 + 3dx3 = (4xy * dy + 6y2 * dy)
2dxy2 + 3dx3 = (4dxy2 + 6dy3)

Solving
2dxy2 + 3dx3 = 4dxy2 + 6dy3

Solving for variable 'd'.

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

Add '-4dxy2' to each side of the equation.
2dxy2 + -4dxy2 + 3dx3 = 4dxy2 + -4dxy2 + 6dy3

Combine like terms: 2dxy2 + -4dxy2 = -2dxy2
-2dxy2 + 3dx3 = 4dxy2 + -4dxy2 + 6dy3

Combine like terms: 4dxy2 + -4dxy2 = 0
-2dxy2 + 3dx3 = 0 + 6dy3
-2dxy2 + 3dx3 = 6dy3

Add '-6dy3' to each side of the equation.
-2dxy2 + 3dx3 + -6dy3 = 6dy3 + -6dy3

Combine like terms: 6dy3 + -6dy3 = 0
-2dxy2 + 3dx3 + -6dy3 = 0

Factor out the Greatest Common Factor (GCF), 'd'.
d(-2xy2 + 3x3 + -6y3) = 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 '(-2xy2 + 3x3 + -6y3)' equal to zero and attempt to solve:

Simplifying
-2xy2 + 3x3 + -6y3 = 0

Solving
-2xy2 + 3x3 + -6y3 = 0

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

Add '2xy2' to each side of the equation.
-2xy2 + 3x3 + 2xy2 + -6y3 = 0 + 2xy2

Reorder the terms:
-2xy2 + 2xy2 + 3x3 + -6y3 = 0 + 2xy2

Combine like terms: -2xy2 + 2xy2 = 0
0 + 3x3 + -6y3 = 0 + 2xy2
3x3 + -6y3 = 0 + 2xy2
Remove the zero:
3x3 + -6y3 = 2xy2

Add '-3x3' to each side of the equation.
3x3 + -3x3 + -6y3 = 2xy2 + -3x3

Combine like terms: 3x3 + -3x3 = 0
0 + -6y3 = 2xy2 + -3x3
-6y3 = 2xy2 + -3x3

Add '6y3' to each side of the equation.
-6y3 + 6y3 = 2xy2 + -3x3 + 6y3

Combine like terms: -6y3 + 6y3 = 0
0 = 2xy2 + -3x3 + 6y3

Simplifying
0 = 2xy2 + -3x3 + 6y3

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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