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

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


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

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

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

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

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

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

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

Solving for variable 'i'.

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

Add '-2z' to each side of the equation.
-2i + 2iz + -1iz2 + 2z + -2z2 + -2z + z3 = 0 + -2z

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

Combine like terms: 2z + -2z = 0
-2i + 2iz + -1iz2 + 0 + -2z2 + z3 = 0 + -2z
-2i + 2iz + -1iz2 + -2z2 + z3 = 0 + -2z
Remove the zero:
-2i + 2iz + -1iz2 + -2z2 + z3 = -2z

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

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

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

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

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

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

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

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

The solution to this equation could not be determined.

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