(4x^2+4y^2)*dx+8xy*dy=0

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Solution for (4x^2+4y^2)*dx+8xy*dy=0 equation: 


Simplifying
(4x2 + 4y2) * dx + 8xy * dy = 0

Reorder the terms for easier multiplication:
dx(4x2 + 4y2) + 8xy * dy = 0
(4x2 * dx + 4y2 * dx) + 8xy * dy = 0

Reorder the terms:
(4dxy2 + 4dx3) + 8xy * dy = 0
(4dxy2 + 4dx3) + 8xy * dy = 0

Multiply xy * dy
4dxy2 + 4dx3 + 8dxy2 = 0

Reorder the terms:
4dxy2 + 8dxy2 + 4dx3 = 0

Combine like terms: 4dxy2 + 8dxy2 = 12dxy2
12dxy2 + 4dx3 = 0

Solving
12dxy2 + 4dx3 = 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), '4dx'.
4dx(3y2 + x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor 'dx' equal to zero and attempt to solve:

Simplifying
dx = 0

Solving
dx = 0

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

Simplifying
dx = 0

The solution to this equation could not be determined.

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

Subproblem 2
Set the factor '(3y2 + x2)' equal to zero and attempt to solve:

Simplifying
3y2 + x2 = 0

Reorder the terms:
x2 + 3y2 = 0

Solving
x2 + 3y2 = 0

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

Add '-1x2' to each side of the equation.
x2 + -1x2 + 3y2 = 0 + -1x2

Combine like terms: x2 + -1x2 = 0
0 + 3y2 = 0 + -1x2
3y2 = 0 + -1x2
Remove the zero:
3y2 = -1x2

Add '-3y2' to each side of the equation.
3y2 + -3y2 = -1x2 + -3y2

Combine like terms: 3y2 + -3y2 = 0
0 = -1x2 + -3y2

Simplifying
0 = -1x2 + -3y2

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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