(yz+2x)dx+(zx-2z)dy+(xy-2y)dz=0

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Solution for (yz+2x)dx+(zx-2z)dy+(xy-2y)dz=0 equation: 


Simplifying
(yz + 2x) * dx + (zx + -2z) * dy + (xy + -2y) * dz = 0

Reorder the terms:
(2x + yz) * dx + (zx + -2z) * dy + (xy + -2y) * dz = 0

Reorder the terms for easier multiplication:
dx(2x + yz) + (zx + -2z) * dy + (xy + -2y) * dz = 0
(2x * dx + yz * dx) + (zx + -2z) * dy + (xy + -2y) * dz = 0

Reorder the terms:
(dxyz + 2dx2) + (zx + -2z) * dy + (xy + -2y) * dz = 0
(dxyz + 2dx2) + (zx + -2z) * dy + (xy + -2y) * dz = 0

Reorder the terms for easier multiplication:
dxyz + 2dx2 + dy(xz + -2z) + (xy + -2y) * dz = 0
dxyz + 2dx2 + (xz * dy + -2z * dy) + (xy + -2y) * dz = 0
dxyz + 2dx2 + (dxyz + -2dyz) + (xy + -2y) * dz = 0

Reorder the terms for easier multiplication:
dxyz + 2dx2 + dxyz + -2dyz + dz(xy + -2y) = 0
dxyz + 2dx2 + dxyz + -2dyz + (xy * dz + -2y * dz) = 0
dxyz + 2dx2 + dxyz + -2dyz + (dxyz + -2dyz) = 0

Reorder the terms:
dxyz + dxyz + dxyz + 2dx2 + -2dyz + -2dyz = 0

Combine like terms: dxyz + dxyz = 2dxyz
2dxyz + dxyz + 2dx2 + -2dyz + -2dyz = 0

Combine like terms: 2dxyz + dxyz = 3dxyz
3dxyz + 2dx2 + -2dyz + -2dyz = 0

Combine like terms: -2dyz + -2dyz = -4dyz
3dxyz + 2dx2 + -4dyz = 0

Solving
3dxyz + 2dx2 + -4dyz = 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(3xyz + 2x2 + -4yz) = 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 '(3xyz + 2x2 + -4yz)' equal to zero and attempt to solve:

Simplifying
3xyz + 2x2 + -4yz = 0

Solving
3xyz + 2x2 + -4yz = 0

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

Add '-3xyz' to each side of the equation.
3xyz + 2x2 + -3xyz + -4yz = 0 + -3xyz

Reorder the terms:
3xyz + -3xyz + 2x2 + -4yz = 0 + -3xyz

Combine like terms: 3xyz + -3xyz = 0
0 + 2x2 + -4yz = 0 + -3xyz
2x2 + -4yz = 0 + -3xyz
Remove the zero:
2x2 + -4yz = -3xyz

Add '-2x2' to each side of the equation.
2x2 + -2x2 + -4yz = -3xyz + -2x2

Combine like terms: 2x2 + -2x2 = 0
0 + -4yz = -3xyz + -2x2
-4yz = -3xyz + -2x2

Add '4yz' to each side of the equation.
-4yz + 4yz = -3xyz + -2x2 + 4yz

Combine like terms: -4yz + 4yz = 0
0 = -3xyz + -2x2 + 4yz

Simplifying
0 = -3xyz + -2x2 + 4yz

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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