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

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


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

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

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

Reorder the terms:
-4iz + 2z2 = (-1i + z)(-2 + z2)

Multiply (-1i + z) * (-2 + z2)
-4iz + 2z2 = (-1i * (-2 + z2) + z(-2 + z2))
-4iz + 2z2 = ((-2 * -1i + z2 * -1i) + z(-2 + z2))
-4iz + 2z2 = ((2i + -1iz2) + z(-2 + z2))
-4iz + 2z2 = (2i + -1iz2 + (-2 * z + z2 * z))
-4iz + 2z2 = (2i + -1iz2 + (-2z + z3))
-4iz + 2z2 = (2i + -1iz2 + -2z + z3)

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

Solving for variable 'i'.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

The solution to this equation could not be determined.

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