z^3-2(1+i)z^2+4(1+i)z+8i=0

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Solution for z^3-2(1+i)z^2+4(1+i)z+8i=0 equation: 


Simplifying
z3 + -2(1 + i) * z2 + 4(1 + i) * z + 8i = 0

Reorder the terms for easier multiplication:
z3 + -2z2(1 + i) + 4(1 + i) * z + 8i = 0
z3 + (1 * -2z2 + i * -2z2) + 4(1 + i) * z + 8i = 0

Reorder the terms:
z3 + (-2iz2 + -2z2) + 4(1 + i) * z + 8i = 0
z3 + (-2iz2 + -2z2) + 4(1 + i) * z + 8i = 0

Reorder the terms for easier multiplication:
z3 + -2iz2 + -2z2 + 4z(1 + i) + 8i = 0
z3 + -2iz2 + -2z2 + (1 * 4z + i * 4z) + 8i = 0

Reorder the terms:
z3 + -2iz2 + -2z2 + (4iz + 4z) + 8i = 0
z3 + -2iz2 + -2z2 + (4iz + 4z) + 8i = 0

Reorder the terms:
8i + 4iz + -2iz2 + 4z + -2z2 + z3 = 0

Solving
8i + 4iz + -2iz2 + 4z + -2z2 + z3 = 0

Solving for variable 'i'.

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

Add '-4z' to each side of the equation.
8i + 4iz + -2iz2 + 4z + -2z2 + -4z + z3 = 0 + -4z

Reorder the terms:
8i + 4iz + -2iz2 + 4z + -4z + -2z2 + z3 = 0 + -4z

Combine like terms: 4z + -4z = 0
8i + 4iz + -2iz2 + 0 + -2z2 + z3 = 0 + -4z
8i + 4iz + -2iz2 + -2z2 + z3 = 0 + -4z
Remove the zero:
8i + 4iz + -2iz2 + -2z2 + z3 = -4z

Add '2z2' to each side of the equation.
8i + 4iz + -2iz2 + -2z2 + 2z2 + z3 = -4z + 2z2

Combine like terms: -2z2 + 2z2 = 0
8i + 4iz + -2iz2 + 0 + z3 = -4z + 2z2
8i + 4iz + -2iz2 + z3 = -4z + 2z2

Add '-1z3' to each side of the equation.
8i + 4iz + -2iz2 + z3 + -1z3 = -4z + 2z2 + -1z3

Combine like terms: z3 + -1z3 = 0
8i + 4iz + -2iz2 + 0 = -4z + 2z2 + -1z3
8i + 4iz + -2iz2 = -4z + 2z2 + -1z3

Reorder the terms:
8i + 4iz + -2iz2 + 4z + -2z2 + z3 = -4z + 4z + 2z2 + -2z2 + -1z3 + z3

Combine like terms: -4z + 4z = 0
8i + 4iz + -2iz2 + 4z + -2z2 + z3 = 0 + 2z2 + -2z2 + -1z3 + z3
8i + 4iz + -2iz2 + 4z + -2z2 + z3 = 2z2 + -2z2 + -1z3 + z3

Combine like terms: 2z2 + -2z2 = 0
8i + 4iz + -2iz2 + 4z + -2z2 + z3 = 0 + -1z3 + z3
8i + 4iz + -2iz2 + 4z + -2z2 + z3 = -1z3 + z3

Combine like terms: -1z3 + z3 = 0
8i + 4iz + -2iz2 + 4z + -2z2 + z3 = 0

The solution to this equation could not be determined.

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