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

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


Simplifying
Z3 + -2z2 + (-2 + 3i) * z + 1 + 3i = 0

Reorder the terms for easier multiplication:
Z3 + -2z2 + z(-2 + 3i) + 1 + 3i = 0
Z3 + -2z2 + (-2 * z + 3i * z) + 1 + 3i = 0

Reorder the terms:
Z3 + -2z2 + (3iz + -2z) + 1 + 3i = 0
Z3 + -2z2 + (3iz + -2z) + 1 + 3i = 0

Reorder the terms:
1 + Z3 + 3i + 3iz + -2z + -2z2 = 0

Solving
1 + Z3 + 3i + 3iz + -2z + -2z2 = 0

Solving for variable 'Z'.

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

Add '-1' to each side of the equation.
1 + Z3 + 3i + 3iz + -2z + -1 + -2z2 = 0 + -1

Reorder the terms:
1 + -1 + Z3 + 3i + 3iz + -2z + -2z2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + Z3 + 3i + 3iz + -2z + -2z2 = 0 + -1
Z3 + 3i + 3iz + -2z + -2z2 = 0 + -1

Combine like terms: 0 + -1 = -1
Z3 + 3i + 3iz + -2z + -2z2 = -1

Add '-3i' to each side of the equation.
Z3 + 3i + 3iz + -2z + -3i + -2z2 = -1 + -3i

Reorder the terms:
Z3 + 3i + -3i + 3iz + -2z + -2z2 = -1 + -3i

Combine like terms: 3i + -3i = 0
Z3 + 0 + 3iz + -2z + -2z2 = -1 + -3i
Z3 + 3iz + -2z + -2z2 = -1 + -3i

Add '-3iz' to each side of the equation.
Z3 + 3iz + -2z + -3iz + -2z2 = -1 + -3i + -3iz

Reorder the terms:
Z3 + 3iz + -3iz + -2z + -2z2 = -1 + -3i + -3iz

Combine like terms: 3iz + -3iz = 0
Z3 + 0 + -2z + -2z2 = -1 + -3i + -3iz
Z3 + -2z + -2z2 = -1 + -3i + -3iz

Add '2z' to each side of the equation.
Z3 + -2z + 2z + -2z2 = -1 + -3i + -3iz + 2z

Combine like terms: -2z + 2z = 0
Z3 + 0 + -2z2 = -1 + -3i + -3iz + 2z
Z3 + -2z2 = -1 + -3i + -3iz + 2z

Add '2z2' to each side of the equation.
Z3 + -2z2 + 2z2 = -1 + -3i + -3iz + 2z + 2z2

Combine like terms: -2z2 + 2z2 = 0
Z3 + 0 = -1 + -3i + -3iz + 2z + 2z2
Z3 = -1 + -3i + -3iz + 2z + 2z2

Simplifying
Z3 = -1 + -3i + -3iz + 2z + 2z2

Reorder the terms:
1 + Z3 + 3i + 3iz + -2z + -2z2 = -1 + -3i + -3iz + 2z + 2z2 + 1 + 3i + 3iz + -2z + -2z2

Reorder the terms:
1 + Z3 + 3i + 3iz + -2z + -2z2 = -1 + 1 + -3i + 3i + -3iz + 3iz + 2z + -2z + 2z2 + -2z2

Combine like terms: -1 + 1 = 0
1 + Z3 + 3i + 3iz + -2z + -2z2 = 0 + -3i + 3i + -3iz + 3iz + 2z + -2z + 2z2 + -2z2
1 + Z3 + 3i + 3iz + -2z + -2z2 = -3i + 3i + -3iz + 3iz + 2z + -2z + 2z2 + -2z2

Combine like terms: -3i + 3i = 0
1 + Z3 + 3i + 3iz + -2z + -2z2 = 0 + -3iz + 3iz + 2z + -2z + 2z2 + -2z2
1 + Z3 + 3i + 3iz + -2z + -2z2 = -3iz + 3iz + 2z + -2z + 2z2 + -2z2

Combine like terms: -3iz + 3iz = 0
1 + Z3 + 3i + 3iz + -2z + -2z2 = 0 + 2z + -2z + 2z2 + -2z2
1 + Z3 + 3i + 3iz + -2z + -2z2 = 2z + -2z + 2z2 + -2z2

Combine like terms: 2z + -2z = 0
1 + Z3 + 3i + 3iz + -2z + -2z2 = 0 + 2z2 + -2z2
1 + Z3 + 3i + 3iz + -2z + -2z2 = 2z2 + -2z2

Combine like terms: 2z2 + -2z2 = 0
1 + Z3 + 3i + 3iz + -2z + -2z2 = 0

The solution to this equation could not be determined.

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