z^3-3z^2+(1+3i)z-6i+2=0

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Solution for z^3-3z^2+(1+3i)z-6i+2=0 equation: 


Simplifying
z3 + -3z2 + (1 + 3i) * z + -6i + 2 = 0

Reorder the terms for easier multiplication:
z3 + -3z2 + z(1 + 3i) + -6i + 2 = 0
z3 + -3z2 + (1 * z + 3i * z) + -6i + 2 = 0

Reorder the terms:
z3 + -3z2 + (3iz + 1z) + -6i + 2 = 0
z3 + -3z2 + (3iz + 1z) + -6i + 2 = 0

Reorder the terms:
2 + -6i + 3iz + 1z + -3z2 + z3 = 0

Solving
2 + -6i + 3iz + 1z + -3z2 + 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 + -6i + 3iz + 1z + -3z2 + -2 + z3 = 0 + -2

Reorder the terms:
2 + -2 + -6i + 3iz + 1z + -3z2 + z3 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -6i + 3iz + 1z + -3z2 + z3 = 0 + -2
-6i + 3iz + 1z + -3z2 + z3 = 0 + -2

Combine like terms: 0 + -2 = -2
-6i + 3iz + 1z + -3z2 + z3 = -2

Add '-1z' to each side of the equation.
-6i + 3iz + 1z + -3z2 + -1z + z3 = -2 + -1z

Reorder the terms:
-6i + 3iz + 1z + -1z + -3z2 + z3 = -2 + -1z

Combine like terms: 1z + -1z = 0
-6i + 3iz + 0 + -3z2 + z3 = -2 + -1z
-6i + 3iz + -3z2 + z3 = -2 + -1z

Add '3z2' to each side of the equation.
-6i + 3iz + -3z2 + 3z2 + z3 = -2 + -1z + 3z2

Combine like terms: -3z2 + 3z2 = 0
-6i + 3iz + 0 + z3 = -2 + -1z + 3z2
-6i + 3iz + z3 = -2 + -1z + 3z2

Add '-1z3' to each side of the equation.
-6i + 3iz + z3 + -1z3 = -2 + -1z + 3z2 + -1z3

Combine like terms: z3 + -1z3 = 0
-6i + 3iz + 0 = -2 + -1z + 3z2 + -1z3
-6i + 3iz = -2 + -1z + 3z2 + -1z3

Reorder the terms:
2 + -6i + 3iz + z + -3z2 + z3 = -2 + -1z + 3z2 + -1z3 + 2 + z + -3z2 + z3

Reorder the terms:
2 + -6i + 3iz + z + -3z2 + z3 = -2 + 2 + -1z + z + 3z2 + -3z2 + -1z3 + z3

Combine like terms: -2 + 2 = 0
2 + -6i + 3iz + z + -3z2 + z3 = 0 + -1z + z + 3z2 + -3z2 + -1z3 + z3
2 + -6i + 3iz + z + -3z2 + z3 = -1z + z + 3z2 + -3z2 + -1z3 + z3

Combine like terms: -1z + z = 0
2 + -6i + 3iz + z + -3z2 + z3 = 0 + 3z2 + -3z2 + -1z3 + z3
2 + -6i + 3iz + z + -3z2 + z3 = 3z2 + -3z2 + -1z3 + z3

Combine like terms: 3z2 + -3z2 = 0
2 + -6i + 3iz + z + -3z2 + z3 = 0 + -1z3 + z3
2 + -6i + 3iz + z + -3z2 + z3 = -1z3 + z3

Combine like terms: -1z3 + z3 = 0
2 + -6i + 3iz + z + -3z2 + z3 = 0

The solution to this equation could not be determined.

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