z^3+(-6+2i)z^2+(12-15i)z+(-9+27i)=0

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Solution for z^3+(-6+2i)z^2+(12-15i)z+(-9+27i)=0 equation: 


Simplifying
z3 + (-6 + 2i) * z2 + (12 + -15i) * z + (-9 + 27i) = 0

Reorder the terms for easier multiplication:
z3 + z2(-6 + 2i) + (12 + -15i) * z + (-9 + 27i) = 0
z3 + (-6 * z2 + 2i * z2) + (12 + -15i) * z + (-9 + 27i) = 0

Reorder the terms:
z3 + (2iz2 + -6z2) + (12 + -15i) * z + (-9 + 27i) = 0
z3 + (2iz2 + -6z2) + (12 + -15i) * z + (-9 + 27i) = 0

Reorder the terms for easier multiplication:
z3 + 2iz2 + -6z2 + z(12 + -15i) + (-9 + 27i) = 0
z3 + 2iz2 + -6z2 + (12 * z + -15i * z) + (-9 + 27i) = 0

Reorder the terms:
z3 + 2iz2 + -6z2 + (-15iz + 12z) + (-9 + 27i) = 0
z3 + 2iz2 + -6z2 + (-15iz + 12z) + (-9 + 27i) = 0

Remove parenthesis around (-9 + 27i)
z3 + 2iz2 + -6z2 + -15iz + 12z + -9 + 27i = 0

Reorder the terms:
-9 + 27i + -15iz + 2iz2 + 12z + -6z2 + z3 = 0

Solving
-9 + 27i + -15iz + 2iz2 + 12z + -6z2 + z3 = 0

Solving for variable 'i'.

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

Add '9' to each side of the equation.
-9 + 27i + -15iz + 2iz2 + 12z + -6z2 + 9 + z3 = 0 + 9

Reorder the terms:
-9 + 9 + 27i + -15iz + 2iz2 + 12z + -6z2 + z3 = 0 + 9

Combine like terms: -9 + 9 = 0
0 + 27i + -15iz + 2iz2 + 12z + -6z2 + z3 = 0 + 9
27i + -15iz + 2iz2 + 12z + -6z2 + z3 = 0 + 9

Combine like terms: 0 + 9 = 9
27i + -15iz + 2iz2 + 12z + -6z2 + z3 = 9

Add '-12z' to each side of the equation.
27i + -15iz + 2iz2 + 12z + -6z2 + -12z + z3 = 9 + -12z

Reorder the terms:
27i + -15iz + 2iz2 + 12z + -12z + -6z2 + z3 = 9 + -12z

Combine like terms: 12z + -12z = 0
27i + -15iz + 2iz2 + 0 + -6z2 + z3 = 9 + -12z
27i + -15iz + 2iz2 + -6z2 + z3 = 9 + -12z

Add '6z2' to each side of the equation.
27i + -15iz + 2iz2 + -6z2 + 6z2 + z3 = 9 + -12z + 6z2

Combine like terms: -6z2 + 6z2 = 0
27i + -15iz + 2iz2 + 0 + z3 = 9 + -12z + 6z2
27i + -15iz + 2iz2 + z3 = 9 + -12z + 6z2

Add '-1z3' to each side of the equation.
27i + -15iz + 2iz2 + z3 + -1z3 = 9 + -12z + 6z2 + -1z3

Combine like terms: z3 + -1z3 = 0
27i + -15iz + 2iz2 + 0 = 9 + -12z + 6z2 + -1z3
27i + -15iz + 2iz2 = 9 + -12z + 6z2 + -1z3

Reorder the terms:
-9 + 27i + -15iz + 2iz2 + 12z + -6z2 + z3 = 9 + -12z + 6z2 + -1z3 + -9 + 12z + -6z2 + z3

Reorder the terms:
-9 + 27i + -15iz + 2iz2 + 12z + -6z2 + z3 = 9 + -9 + -12z + 12z + 6z2 + -6z2 + -1z3 + z3

Combine like terms: 9 + -9 = 0
-9 + 27i + -15iz + 2iz2 + 12z + -6z2 + z3 = 0 + -12z + 12z + 6z2 + -6z2 + -1z3 + z3
-9 + 27i + -15iz + 2iz2 + 12z + -6z2 + z3 = -12z + 12z + 6z2 + -6z2 + -1z3 + z3

Combine like terms: -12z + 12z = 0
-9 + 27i + -15iz + 2iz2 + 12z + -6z2 + z3 = 0 + 6z2 + -6z2 + -1z3 + z3
-9 + 27i + -15iz + 2iz2 + 12z + -6z2 + z3 = 6z2 + -6z2 + -1z3 + z3

Combine like terms: 6z2 + -6z2 = 0
-9 + 27i + -15iz + 2iz2 + 12z + -6z2 + z3 = 0 + -1z3 + z3
-9 + 27i + -15iz + 2iz2 + 12z + -6z2 + z3 = -1z3 + z3

Combine like terms: -1z3 + z3 = 0
-9 + 27i + -15iz + 2iz2 + 12z + -6z2 + z3 = 0

The solution to this equation could not be determined.

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