(z-2)(z-(1+i))(z+(1-i))=0

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Solution for (z-2)(z-(1+i))(z+(1-i))=0 equation: 


Simplifying
(z + -2)(z + -1(1 + i))(z + (1 + -1i)) = 0

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

Reorder the terms:
(-2 + z)(-1 + -1i + z)(z + (1 + -1i)) = 0

Remove parenthesis around (1 + -1i)
(-2 + z)(-1 + -1i + z)(z + 1 + -1i) = 0

Reorder the terms:
(-2 + z)(-1 + -1i + z)(1 + -1i + z) = 0

Multiply (-2 + z) * (-1 + -1i + z)
(-2(-1 + -1i + z) + z(-1 + -1i + z))(1 + -1i + z) = 0
((-1 * -2 + -1i * -2 + z * -2) + z(-1 + -1i + z))(1 + -1i + z) = 0
((2 + 2i + -2z) + z(-1 + -1i + z))(1 + -1i + z) = 0
(2 + 2i + -2z + (-1 * z + -1i * z + z * z))(1 + -1i + z) = 0

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

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

Combine like terms: -2z + -1z = -3z
(2 + 2i + -1iz + -3z + z2)(1 + -1i + z) = 0

Multiply (2 + 2i + -1iz + -3z + z2) * (1 + -1i + z)
(2(1 + -1i + z) + 2i * (1 + -1i + z) + -1iz * (1 + -1i + z) + -3z * (1 + -1i + z) + z2(1 + -1i + z)) = 0
((1 * 2 + -1i * 2 + z * 2) + 2i * (1 + -1i + z) + -1iz * (1 + -1i + z) + -3z * (1 + -1i + z) + z2(1 + -1i + z)) = 0
((2 + -2i + 2z) + 2i * (1 + -1i + z) + -1iz * (1 + -1i + z) + -3z * (1 + -1i + z) + z2(1 + -1i + z)) = 0
(2 + -2i + 2z + (1 * 2i + -1i * 2i + z * 2i) + -1iz * (1 + -1i + z) + -3z * (1 + -1i + z) + z2(1 + -1i + z)) = 0

Reorder the terms:
(2 + -2i + 2z + (2i + 2iz + -2i2) + -1iz * (1 + -1i + z) + -3z * (1 + -1i + z) + z2(1 + -1i + z)) = 0
(2 + -2i + 2z + (2i + 2iz + -2i2) + -1iz * (1 + -1i + z) + -3z * (1 + -1i + z) + z2(1 + -1i + z)) = 0
(2 + -2i + 2z + 2i + 2iz + -2i2 + (1 * -1iz + -1i * -1iz + z * -1iz) + -3z * (1 + -1i + z) + z2(1 + -1i + z)) = 0

Reorder the terms:
(2 + -2i + 2z + 2i + 2iz + -2i2 + (-1iz + -1iz2 + 1i2z) + -3z * (1 + -1i + z) + z2(1 + -1i + z)) = 0
(2 + -2i + 2z + 2i + 2iz + -2i2 + (-1iz + -1iz2 + 1i2z) + -3z * (1 + -1i + z) + z2(1 + -1i + z)) = 0
(2 + -2i + 2z + 2i + 2iz + -2i2 + -1iz + -1iz2 + 1i2z + (1 * -3z + -1i * -3z + z * -3z) + z2(1 + -1i + z)) = 0

Reorder the terms:
(2 + -2i + 2z + 2i + 2iz + -2i2 + -1iz + -1iz2 + 1i2z + (3iz + -3z + -3z2) + z2(1 + -1i + z)) = 0
(2 + -2i + 2z + 2i + 2iz + -2i2 + -1iz + -1iz2 + 1i2z + (3iz + -3z + -3z2) + z2(1 + -1i + z)) = 0
(2 + -2i + 2z + 2i + 2iz + -2i2 + -1iz + -1iz2 + 1i2z + 3iz + -3z + -3z2 + (1 * z2 + -1i * z2 + z * z2)) = 0

Reorder the terms:
(2 + -2i + 2z + 2i + 2iz + -2i2 + -1iz + -1iz2 + 1i2z + 3iz + -3z + -3z2 + (-1iz2 + 1z2 + z3)) = 0
(2 + -2i + 2z + 2i + 2iz + -2i2 + -1iz + -1iz2 + 1i2z + 3iz + -3z + -3z2 + (-1iz2 + 1z2 + z3)) = 0

Reorder the terms:
(2 + -2i + 2i + 2iz + -1iz + 3iz + -1iz2 + -1iz2 + -2i2 + 1i2z + 2z + -3z + -3z2 + 1z2 + z3) = 0

Combine like terms: -2i + 2i = 0
(2 + 0 + 2iz + -1iz + 3iz + -1iz2 + -1iz2 + -2i2 + 1i2z + 2z + -3z + -3z2 + 1z2 + z3) = 0
(2 + 2iz + -1iz + 3iz + -1iz2 + -1iz2 + -2i2 + 1i2z + 2z + -3z + -3z2 + 1z2 + z3) = 0

Combine like terms: 2iz + -1iz = 1iz
(2 + 1iz + 3iz + -1iz2 + -1iz2 + -2i2 + 1i2z + 2z + -3z + -3z2 + 1z2 + z3) = 0

Combine like terms: 1iz + 3iz = 4iz
(2 + 4iz + -1iz2 + -1iz2 + -2i2 + 1i2z + 2z + -3z + -3z2 + 1z2 + z3) = 0

Combine like terms: -1iz2 + -1iz2 = -2iz2
(2 + 4iz + -2iz2 + -2i2 + 1i2z + 2z + -3z + -3z2 + 1z2 + z3) = 0

Combine like terms: 2z + -3z = -1z
(2 + 4iz + -2iz2 + -2i2 + 1i2z + -1z + -3z2 + 1z2 + z3) = 0

Combine like terms: -3z2 + 1z2 = -2z2
(2 + 4iz + -2iz2 + -2i2 + 1i2z + -1z + -2z2 + z3) = 0

Solving
2 + 4iz + -2iz2 + -2i2 + 1i2z + -1z + -2z2 + z3 = 0

Solving for variable 'i'.

The solution to this equation could not be determined.

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