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

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


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

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

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

Multiply (8 + -4z + z2) * (-2i + z)
(8(-2i + z) + -4z * (-2i + z) + z2(-2i + z)) = 0
((-2i * 8 + z * 8) + -4z * (-2i + z) + z2(-2i + z)) = 0
((-16i + 8z) + -4z * (-2i + z) + z2(-2i + z)) = 0
(-16i + 8z + (-2i * -4z + z * -4z) + z2(-2i + z)) = 0
(-16i + 8z + (8iz + -4z2) + z2(-2i + z)) = 0
(-16i + 8z + 8iz + -4z2 + (-2i * z2 + z * z2)) = 0
(-16i + 8z + 8iz + -4z2 + (-2iz2 + z3)) = 0

Reorder the terms:
(-16i + 8iz + -2iz2 + 8z + -4z2 + z3) = 0
(-16i + 8iz + -2iz2 + 8z + -4z2 + z3) = 0

Solving
-16i + 8iz + -2iz2 + 8z + -4z2 + z3 = 0

Solving for variable 'i'.

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

Add '-8z' to each side of the equation.
-16i + 8iz + -2iz2 + 8z + -4z2 + -8z + z3 = 0 + -8z

Reorder the terms:
-16i + 8iz + -2iz2 + 8z + -8z + -4z2 + z3 = 0 + -8z

Combine like terms: 8z + -8z = 0
-16i + 8iz + -2iz2 + 0 + -4z2 + z3 = 0 + -8z
-16i + 8iz + -2iz2 + -4z2 + z3 = 0 + -8z
Remove the zero:
-16i + 8iz + -2iz2 + -4z2 + z3 = -8z

Add '4z2' to each side of the equation.
-16i + 8iz + -2iz2 + -4z2 + 4z2 + z3 = -8z + 4z2

Combine like terms: -4z2 + 4z2 = 0
-16i + 8iz + -2iz2 + 0 + z3 = -8z + 4z2
-16i + 8iz + -2iz2 + z3 = -8z + 4z2

Add '-1z3' to each side of the equation.
-16i + 8iz + -2iz2 + z3 + -1z3 = -8z + 4z2 + -1z3

Combine like terms: z3 + -1z3 = 0
-16i + 8iz + -2iz2 + 0 = -8z + 4z2 + -1z3
-16i + 8iz + -2iz2 = -8z + 4z2 + -1z3

Reorder the terms:
-16i + 8iz + -2iz2 + 8z + -4z2 + z3 = -8z + 8z + 4z2 + -4z2 + -1z3 + z3

Combine like terms: -8z + 8z = 0
-16i + 8iz + -2iz2 + 8z + -4z2 + z3 = 0 + 4z2 + -4z2 + -1z3 + z3
-16i + 8iz + -2iz2 + 8z + -4z2 + z3 = 4z2 + -4z2 + -1z3 + z3

Combine like terms: 4z2 + -4z2 = 0
-16i + 8iz + -2iz2 + 8z + -4z2 + z3 = 0 + -1z3 + z3
-16i + 8iz + -2iz2 + 8z + -4z2 + z3 = -1z3 + z3

Combine like terms: -1z3 + z3 = 0
-16i + 8iz + -2iz2 + 8z + -4z2 + z3 = 0

The solution to this equation could not be determined.

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