z^3+(1-2i)z^2-6z+(4+2i)=0

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Solution for z^3+(1-2i)z^2-6z+(4+2i)=0 equation: 


Simplifying
z3 + (1 + -2i) * z2 + -6z + (4 + 2i) = 0

Reorder the terms for easier multiplication:
z3 + z2(1 + -2i) + -6z + (4 + 2i) = 0
z3 + (1 * z2 + -2i * z2) + -6z + (4 + 2i) = 0

Reorder the terms:
z3 + (-2iz2 + 1z2) + -6z + (4 + 2i) = 0
z3 + (-2iz2 + 1z2) + -6z + (4 + 2i) = 0

Remove parenthesis around (4 + 2i)
z3 + -2iz2 + 1z2 + -6z + 4 + 2i = 0

Reorder the terms:
4 + 2i + -2iz2 + -6z + 1z2 + z3 = 0

Solving
4 + 2i + -2iz2 + -6z + 1z2 + 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 + 2i + -2iz2 + -6z + 1z2 + -4 + z3 = 0 + -4

Reorder the terms:
4 + -4 + 2i + -2iz2 + -6z + 1z2 + z3 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 2i + -2iz2 + -6z + 1z2 + z3 = 0 + -4
2i + -2iz2 + -6z + 1z2 + z3 = 0 + -4

Combine like terms: 0 + -4 = -4
2i + -2iz2 + -6z + 1z2 + z3 = -4

Add '6z' to each side of the equation.
2i + -2iz2 + -6z + 1z2 + 6z + z3 = -4 + 6z

Reorder the terms:
2i + -2iz2 + -6z + 6z + 1z2 + z3 = -4 + 6z

Combine like terms: -6z + 6z = 0
2i + -2iz2 + 0 + 1z2 + z3 = -4 + 6z
2i + -2iz2 + 1z2 + z3 = -4 + 6z

Add '-1z2' to each side of the equation.
2i + -2iz2 + 1z2 + -1z2 + z3 = -4 + 6z + -1z2

Combine like terms: 1z2 + -1z2 = 0
2i + -2iz2 + 0 + z3 = -4 + 6z + -1z2
2i + -2iz2 + z3 = -4 + 6z + -1z2

Add '-1z3' to each side of the equation.
2i + -2iz2 + z3 + -1z3 = -4 + 6z + -1z2 + -1z3

Combine like terms: z3 + -1z3 = 0
2i + -2iz2 + 0 = -4 + 6z + -1z2 + -1z3
2i + -2iz2 = -4 + 6z + -1z2 + -1z3

Reorder the terms:
4 + 2i + -2iz2 + -6z + z2 + z3 = -4 + 6z + -1z2 + -1z3 + 4 + -6z + z2 + z3

Reorder the terms:
4 + 2i + -2iz2 + -6z + z2 + z3 = -4 + 4 + 6z + -6z + -1z2 + z2 + -1z3 + z3

Combine like terms: -4 + 4 = 0
4 + 2i + -2iz2 + -6z + z2 + z3 = 0 + 6z + -6z + -1z2 + z2 + -1z3 + z3
4 + 2i + -2iz2 + -6z + z2 + z3 = 6z + -6z + -1z2 + z2 + -1z3 + z3

Combine like terms: 6z + -6z = 0
4 + 2i + -2iz2 + -6z + z2 + z3 = 0 + -1z2 + z2 + -1z3 + z3
4 + 2i + -2iz2 + -6z + z2 + z3 = -1z2 + z2 + -1z3 + z3

Combine like terms: -1z2 + z2 = 0
4 + 2i + -2iz2 + -6z + z2 + z3 = 0 + -1z3 + z3
4 + 2i + -2iz2 + -6z + z2 + z3 = -1z3 + z3

Combine like terms: -1z3 + z3 = 0
4 + 2i + -2iz2 + -6z + z2 + z3 = 0

The solution to this equation could not be determined.

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