2Z(3Z+1)dw+(1-2w)dZ=0

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Solution for 2Z(3Z+1)dw+(1-2w)dZ=0 equation: 


Simplifying
2Z(3Z + 1) * dw + (1 + -2w) * dZ = 0

Reorder the terms:
2Z(1 + 3Z) * dw + (1 + -2w) * dZ = 0

Reorder the terms for easier multiplication:
2Z * dw(1 + 3Z) + (1 + -2w) * dZ = 0

Multiply Z * dw
2dwZ(1 + 3Z) + (1 + -2w) * dZ = 0
(1 * 2dwZ + 3Z * 2dwZ) + (1 + -2w) * dZ = 0
(2dwZ + 6dwZ2) + (1 + -2w) * dZ = 0

Reorder the terms for easier multiplication:
2dwZ + 6dwZ2 + dZ(1 + -2w) = 0
2dwZ + 6dwZ2 + (1 * dZ + -2w * dZ) = 0
2dwZ + 6dwZ2 + (1dZ + -2dwZ) = 0

Reorder the terms:
1dZ + 2dwZ + -2dwZ + 6dwZ2 = 0

Combine like terms: 2dwZ + -2dwZ = 0
1dZ + 0 + 6dwZ2 = 0
1dZ + 6dwZ2 = 0

Solving
1dZ + 6dwZ2 = 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), 'dZ'.
dZ(1 + 6wZ) = 0


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

Simplifying
dZ = 0

Solving
dZ = 0

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

Simplifying
dZ = 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 '(1 + 6wZ)' equal to zero and attempt to solve:

Simplifying
1 + 6wZ = 0

Solving
1 + 6wZ = 0

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

Add '-1' to each side of the equation.
1 + -1 + 6wZ = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 6wZ = 0 + -1
6wZ = 0 + -1

Combine like terms: 0 + -1 = -1
6wZ = -1

Add '-6wZ' to each side of the equation.
6wZ + -6wZ = -1 + -6wZ

Combine like terms: 6wZ + -6wZ = 0
0 = -1 + -6wZ

Simplifying
0 = -1 + -6wZ

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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