z^3-(2-3i)z^2+(4-6i)z+12i=0

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Solution for z^3-(2-3i)z^2+(4-6i)z+12i=0 equation: 


Simplifying
z3 + -1(2 + -3i) * z2 + (4 + -6i) * z + 12i = 0

Reorder the terms for easier multiplication:
z3 + -1z2(2 + -3i) + (4 + -6i) * z + 12i = 0
z3 + (2 * -1z2 + -3i * -1z2) + (4 + -6i) * z + 12i = 0

Reorder the terms:
z3 + (3iz2 + -2z2) + (4 + -6i) * z + 12i = 0
z3 + (3iz2 + -2z2) + (4 + -6i) * z + 12i = 0

Reorder the terms for easier multiplication:
z3 + 3iz2 + -2z2 + z(4 + -6i) + 12i = 0
z3 + 3iz2 + -2z2 + (4 * z + -6i * z) + 12i = 0

Reorder the terms:
z3 + 3iz2 + -2z2 + (-6iz + 4z) + 12i = 0
z3 + 3iz2 + -2z2 + (-6iz + 4z) + 12i = 0

Reorder the terms:
12i + -6iz + 3iz2 + 4z + -2z2 + z3 = 0

Solving
12i + -6iz + 3iz2 + 4z + -2z2 + z3 = 0

Solving for variable 'i'.

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

Add '-4z' to each side of the equation.
12i + -6iz + 3iz2 + 4z + -2z2 + -4z + z3 = 0 + -4z

Reorder the terms:
12i + -6iz + 3iz2 + 4z + -4z + -2z2 + z3 = 0 + -4z

Combine like terms: 4z + -4z = 0
12i + -6iz + 3iz2 + 0 + -2z2 + z3 = 0 + -4z
12i + -6iz + 3iz2 + -2z2 + z3 = 0 + -4z
Remove the zero:
12i + -6iz + 3iz2 + -2z2 + z3 = -4z

Add '2z2' to each side of the equation.
12i + -6iz + 3iz2 + -2z2 + 2z2 + z3 = -4z + 2z2

Combine like terms: -2z2 + 2z2 = 0
12i + -6iz + 3iz2 + 0 + z3 = -4z + 2z2
12i + -6iz + 3iz2 + z3 = -4z + 2z2

Add '-1z3' to each side of the equation.
12i + -6iz + 3iz2 + z3 + -1z3 = -4z + 2z2 + -1z3

Combine like terms: z3 + -1z3 = 0
12i + -6iz + 3iz2 + 0 = -4z + 2z2 + -1z3
12i + -6iz + 3iz2 = -4z + 2z2 + -1z3

Reorder the terms:
12i + -6iz + 3iz2 + 4z + -2z2 + z3 = -4z + 4z + 2z2 + -2z2 + -1z3 + z3

Combine like terms: -4z + 4z = 0
12i + -6iz + 3iz2 + 4z + -2z2 + z3 = 0 + 2z2 + -2z2 + -1z3 + z3
12i + -6iz + 3iz2 + 4z + -2z2 + z3 = 2z2 + -2z2 + -1z3 + z3

Combine like terms: 2z2 + -2z2 = 0
12i + -6iz + 3iz2 + 4z + -2z2 + z3 = 0 + -1z3 + z3
12i + -6iz + 3iz2 + 4z + -2z2 + z3 = -1z3 + z3

Combine like terms: -1z3 + z3 = 0
12i + -6iz + 3iz2 + 4z + -2z2 + z3 = 0

The solution to this equation could not be determined.

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