z^3-2(1+i)z^2-2(1-2i)z+4=0

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Solution for z^3-2(1+i)z^2-2(1-2i)z+4=0 equation: 


Simplifying
z3 + -2(1 + i) * z2 + -2(1 + -2i) * z + 4 = 0

Reorder the terms for easier multiplication:
z3 + -2z2(1 + i) + -2(1 + -2i) * z + 4 = 0
z3 + (1 * -2z2 + i * -2z2) + -2(1 + -2i) * z + 4 = 0

Reorder the terms:
z3 + (-2iz2 + -2z2) + -2(1 + -2i) * z + 4 = 0
z3 + (-2iz2 + -2z2) + -2(1 + -2i) * z + 4 = 0

Reorder the terms for easier multiplication:
z3 + -2iz2 + -2z2 + -2z(1 + -2i) + 4 = 0
z3 + -2iz2 + -2z2 + (1 * -2z + -2i * -2z) + 4 = 0

Reorder the terms:
z3 + -2iz2 + -2z2 + (4iz + -2z) + 4 = 0
z3 + -2iz2 + -2z2 + (4iz + -2z) + 4 = 0

Reorder the terms:
4 + 4iz + -2iz2 + -2z + -2z2 + z3 = 0

Solving
4 + 4iz + -2iz2 + -2z + -2z2 + z3 = 0

Solving for variable 'i'.

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

Add '-4' to each side of the equation.
4 + 4iz + -2iz2 + -2z + -2z2 + -4 + z3 = 0 + -4

Reorder the terms:
4 + -4 + 4iz + -2iz2 + -2z + -2z2 + z3 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 4iz + -2iz2 + -2z + -2z2 + z3 = 0 + -4
4iz + -2iz2 + -2z + -2z2 + z3 = 0 + -4

Combine like terms: 0 + -4 = -4
4iz + -2iz2 + -2z + -2z2 + z3 = -4

Add '2z' to each side of the equation.
4iz + -2iz2 + -2z + -2z2 + 2z + z3 = -4 + 2z

Reorder the terms:
4iz + -2iz2 + -2z + 2z + -2z2 + z3 = -4 + 2z

Combine like terms: -2z + 2z = 0
4iz + -2iz2 + 0 + -2z2 + z3 = -4 + 2z
4iz + -2iz2 + -2z2 + z3 = -4 + 2z

Add '2z2' to each side of the equation.
4iz + -2iz2 + -2z2 + 2z2 + z3 = -4 + 2z + 2z2

Combine like terms: -2z2 + 2z2 = 0
4iz + -2iz2 + 0 + z3 = -4 + 2z + 2z2
4iz + -2iz2 + z3 = -4 + 2z + 2z2

Add '-1z3' to each side of the equation.
4iz + -2iz2 + z3 + -1z3 = -4 + 2z + 2z2 + -1z3

Combine like terms: z3 + -1z3 = 0
4iz + -2iz2 + 0 = -4 + 2z + 2z2 + -1z3
4iz + -2iz2 = -4 + 2z + 2z2 + -1z3

Reorder the terms:
4 + 4iz + -2iz2 + -2z + -2z2 + z3 = -4 + 2z + 2z2 + -1z3 + 4 + -2z + -2z2 + z3

Reorder the terms:
4 + 4iz + -2iz2 + -2z + -2z2 + z3 = -4 + 4 + 2z + -2z + 2z2 + -2z2 + -1z3 + z3

Combine like terms: -4 + 4 = 0
4 + 4iz + -2iz2 + -2z + -2z2 + z3 = 0 + 2z + -2z + 2z2 + -2z2 + -1z3 + z3
4 + 4iz + -2iz2 + -2z + -2z2 + z3 = 2z + -2z + 2z2 + -2z2 + -1z3 + z3

Combine like terms: 2z + -2z = 0
4 + 4iz + -2iz2 + -2z + -2z2 + z3 = 0 + 2z2 + -2z2 + -1z3 + z3
4 + 4iz + -2iz2 + -2z + -2z2 + z3 = 2z2 + -2z2 + -1z3 + z3

Combine like terms: 2z2 + -2z2 = 0
4 + 4iz + -2iz2 + -2z + -2z2 + z3 = 0 + -1z3 + z3
4 + 4iz + -2iz2 + -2z + -2z2 + z3 = -1z3 + z3

Combine like terms: -1z3 + z3 = 0
4 + 4iz + -2iz2 + -2z + -2z2 + z3 = 0

The solution to this equation could not be determined.

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