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

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


Simplifying
z3 + (1 + -3i) * z2 + -1(2 + 3i) * z + -2 = 0

Reorder the terms for easier multiplication:
z3 + z2(1 + -3i) + -1(2 + 3i) * z + -2 = 0
z3 + (1 * z2 + -3i * z2) + -1(2 + 3i) * z + -2 = 0

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

Reorder the terms for easier multiplication:
z3 + -3iz2 + 1z2 + -1z(2 + 3i) + -2 = 0
z3 + -3iz2 + 1z2 + (2 * -1z + 3i * -1z) + -2 = 0

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

Reorder the terms:
-2 + -3iz + -3iz2 + -2z + 1z2 + z3 = 0

Solving
-2 + -3iz + -3iz2 + -2z + 1z2 + z3 = 0

Solving for variable 'i'.

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

Add '2' to each side of the equation.
-2 + -3iz + -3iz2 + -2z + 1z2 + 2 + z3 = 0 + 2

Reorder the terms:
-2 + 2 + -3iz + -3iz2 + -2z + 1z2 + z3 = 0 + 2

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

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

Add '2z' to each side of the equation.
-3iz + -3iz2 + -2z + 1z2 + 2z + z3 = 2 + 2z

Reorder the terms:
-3iz + -3iz2 + -2z + 2z + 1z2 + z3 = 2 + 2z

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

Add '-1z2' to each side of the equation.
-3iz + -3iz2 + 1z2 + -1z2 + z3 = 2 + 2z + -1z2

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

Add '-1z3' to each side of the equation.
-3iz + -3iz2 + z3 + -1z3 = 2 + 2z + -1z2 + -1z3

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

Reorder the terms:
-2 + -3iz + -3iz2 + -2z + z2 + z3 = 2 + 2z + -1z2 + -1z3 + -2 + -2z + z2 + z3

Reorder the terms:
-2 + -3iz + -3iz2 + -2z + z2 + z3 = 2 + -2 + 2z + -2z + -1z2 + z2 + -1z3 + z3

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

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

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

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

The solution to this equation could not be determined.

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