dy(3x^2+y^2)+dx(x^2+3y^2)=0

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Solution for dy(3x^2+y^2)+dx(x^2+3y^2)=0 equation: 


Simplifying
dy(3x2 + y2) + dx(x2 + 3y2) = 0
(3x2 * dy + y2 * dy) + dx(x2 + 3y2) = 0
(3dx2y + dy3) + dx(x2 + 3y2) = 0
3dx2y + dy3 + (x2 * dx + 3y2 * dx) = 0

Reorder the terms:
3dx2y + dy3 + (3dxy2 + dx3) = 0
3dx2y + dy3 + (3dxy2 + dx3) = 0

Reorder the terms:
3dxy2 + 3dx2y + dx3 + dy3 = 0

Solving
3dxy2 + 3dx2y + dx3 + dy3 = 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), 'd'.
d(3xy2 + 3x2y + x3 + y3) = 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 '(3xy2 + 3x2y + x3 + y3)' equal to zero and attempt to solve:

Simplifying
3xy2 + 3x2y + x3 + y3 = 0

Solving
3xy2 + 3x2y + x3 + y3 = 0

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

Add '-3xy2' to each side of the equation.
3xy2 + 3x2y + x3 + -3xy2 + y3 = 0 + -3xy2

Reorder the terms:
3xy2 + -3xy2 + 3x2y + x3 + y3 = 0 + -3xy2

Combine like terms: 3xy2 + -3xy2 = 0
0 + 3x2y + x3 + y3 = 0 + -3xy2
3x2y + x3 + y3 = 0 + -3xy2
Remove the zero:
3x2y + x3 + y3 = -3xy2

Add '-3x2y' to each side of the equation.
3x2y + x3 + -3x2y + y3 = -3xy2 + -3x2y

Reorder the terms:
3x2y + -3x2y + x3 + y3 = -3xy2 + -3x2y

Combine like terms: 3x2y + -3x2y = 0
0 + x3 + y3 = -3xy2 + -3x2y
x3 + y3 = -3xy2 + -3x2y

Add '-1x3' to each side of the equation.
x3 + -1x3 + y3 = -3xy2 + -3x2y + -1x3

Combine like terms: x3 + -1x3 = 0
0 + y3 = -3xy2 + -3x2y + -1x3
y3 = -3xy2 + -3x2y + -1x3

Add '-1y3' to each side of the equation.
y3 + -1y3 = -3xy2 + -3x2y + -1x3 + -1y3

Combine like terms: y3 + -1y3 = 0
0 = -3xy2 + -3x2y + -1x3 + -1y3

Simplifying
0 = -3xy2 + -3x2y + -1x3 + -1y3

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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