(2+4i)z^2+2z+6+6i=0

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Solution for (2+4i)z^2+2z+6+6i=0 equation: 


Simplifying
(2 + 4i) * z2 + 2z + 6 + 6i = 0

Reorder the terms for easier multiplication:
z2(2 + 4i) + 2z + 6 + 6i = 0
(2 * z2 + 4i * z2) + 2z + 6 + 6i = 0

Reorder the terms:
(4iz2 + 2z2) + 2z + 6 + 6i = 0
(4iz2 + 2z2) + 2z + 6 + 6i = 0

Reorder the terms:
6 + 6i + 4iz2 + 2z + 2z2 = 0

Solving
6 + 6i + 4iz2 + 2z + 2z2 = 0

Solving for variable 'i'.

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

Add '-6' to each side of the equation.
6 + 6i + 4iz2 + 2z + -6 + 2z2 = 0 + -6

Reorder the terms:
6 + -6 + 6i + 4iz2 + 2z + 2z2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + 6i + 4iz2 + 2z + 2z2 = 0 + -6
6i + 4iz2 + 2z + 2z2 = 0 + -6

Combine like terms: 0 + -6 = -6
6i + 4iz2 + 2z + 2z2 = -6

Add '-2z' to each side of the equation.
6i + 4iz2 + 2z + -2z + 2z2 = -6 + -2z

Combine like terms: 2z + -2z = 0
6i + 4iz2 + 0 + 2z2 = -6 + -2z
6i + 4iz2 + 2z2 = -6 + -2z

Add '-2z2' to each side of the equation.
6i + 4iz2 + 2z2 + -2z2 = -6 + -2z + -2z2

Combine like terms: 2z2 + -2z2 = 0
6i + 4iz2 + 0 = -6 + -2z + -2z2
6i + 4iz2 = -6 + -2z + -2z2

Reorder the terms:
6 + 6i + 4iz2 + 2z + 2z2 = -6 + -2z + -2z2 + 6 + 2z + 2z2

Reorder the terms:
6 + 6i + 4iz2 + 2z + 2z2 = -6 + 6 + -2z + 2z + -2z2 + 2z2

Combine like terms: -6 + 6 = 0
6 + 6i + 4iz2 + 2z + 2z2 = 0 + -2z + 2z + -2z2 + 2z2
6 + 6i + 4iz2 + 2z + 2z2 = -2z + 2z + -2z2 + 2z2

Combine like terms: -2z + 2z = 0
6 + 6i + 4iz2 + 2z + 2z2 = 0 + -2z2 + 2z2
6 + 6i + 4iz2 + 2z + 2z2 = -2z2 + 2z2

Combine like terms: -2z2 + 2z2 = 0
6 + 6i + 4iz2 + 2z + 2z2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + 3i + 2iz2 + z + z2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(3 + 3i + 2iz2 + z + z2)' equal to zero and attempt to solve:

Simplifying
3 + 3i + 2iz2 + z + z2 = 0

Solving
3 + 3i + 2iz2 + z + z2 = 0

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

Add '-3' to each side of the equation.
3 + 3i + 2iz2 + z + -3 + z2 = 0 + -3

Reorder the terms:
3 + -3 + 3i + 2iz2 + z + z2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 3i + 2iz2 + z + z2 = 0 + -3
3i + 2iz2 + z + z2 = 0 + -3

Combine like terms: 0 + -3 = -3
3i + 2iz2 + z + z2 = -3

Add '-1z' to each side of the equation.
3i + 2iz2 + z + -1z + z2 = -3 + -1z

Combine like terms: z + -1z = 0
3i + 2iz2 + 0 + z2 = -3 + -1z
3i + 2iz2 + z2 = -3 + -1z

Add '-1z2' to each side of the equation.
3i + 2iz2 + z2 + -1z2 = -3 + -1z + -1z2

Combine like terms: z2 + -1z2 = 0
3i + 2iz2 + 0 = -3 + -1z + -1z2
3i + 2iz2 = -3 + -1z + -1z2

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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