z^3+(4-i)z^2+(5-4i)z-5i=0

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Solution for z^3+(4-i)z^2+(5-4i)z-5i=0 equation: 


Simplifying
z3 + (4 + -1i) * z2 + (5 + -4i) * z + -5i = 0

Reorder the terms for easier multiplication:
z3 + z2(4 + -1i) + (5 + -4i) * z + -5i = 0
z3 + (4 * z2 + -1i * z2) + (5 + -4i) * z + -5i = 0

Reorder the terms:
z3 + (-1iz2 + 4z2) + (5 + -4i) * z + -5i = 0
z3 + (-1iz2 + 4z2) + (5 + -4i) * z + -5i = 0

Reorder the terms for easier multiplication:
z3 + -1iz2 + 4z2 + z(5 + -4i) + -5i = 0
z3 + -1iz2 + 4z2 + (5 * z + -4i * z) + -5i = 0

Reorder the terms:
z3 + -1iz2 + 4z2 + (-4iz + 5z) + -5i = 0
z3 + -1iz2 + 4z2 + (-4iz + 5z) + -5i = 0

Reorder the terms:
-5i + -4iz + -1iz2 + 5z + 4z2 + z3 = 0

Solving
-5i + -4iz + -1iz2 + 5z + 4z2 + z3 = 0

Solving for variable 'i'.

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

Add '-5z' to each side of the equation.
-5i + -4iz + -1iz2 + 5z + 4z2 + -5z + z3 = 0 + -5z

Reorder the terms:
-5i + -4iz + -1iz2 + 5z + -5z + 4z2 + z3 = 0 + -5z

Combine like terms: 5z + -5z = 0
-5i + -4iz + -1iz2 + 0 + 4z2 + z3 = 0 + -5z
-5i + -4iz + -1iz2 + 4z2 + z3 = 0 + -5z
Remove the zero:
-5i + -4iz + -1iz2 + 4z2 + z3 = -5z

Add '-4z2' to each side of the equation.
-5i + -4iz + -1iz2 + 4z2 + -4z2 + z3 = -5z + -4z2

Combine like terms: 4z2 + -4z2 = 0
-5i + -4iz + -1iz2 + 0 + z3 = -5z + -4z2
-5i + -4iz + -1iz2 + z3 = -5z + -4z2

Add '-1z3' to each side of the equation.
-5i + -4iz + -1iz2 + z3 + -1z3 = -5z + -4z2 + -1z3

Combine like terms: z3 + -1z3 = 0
-5i + -4iz + -1iz2 + 0 = -5z + -4z2 + -1z3
-5i + -4iz + -1iz2 = -5z + -4z2 + -1z3

Reorder the terms:
-5i + -4iz + -1iz2 + 5z + 4z2 + z3 = -5z + 5z + -4z2 + 4z2 + -1z3 + z3

Combine like terms: -5z + 5z = 0
-5i + -4iz + -1iz2 + 5z + 4z2 + z3 = 0 + -4z2 + 4z2 + -1z3 + z3
-5i + -4iz + -1iz2 + 5z + 4z2 + z3 = -4z2 + 4z2 + -1z3 + z3

Combine like terms: -4z2 + 4z2 = 0
-5i + -4iz + -1iz2 + 5z + 4z2 + z3 = 0 + -1z3 + z3
-5i + -4iz + -1iz2 + 5z + 4z2 + z3 = -1z3 + z3

Combine like terms: -1z3 + z3 = 0
-5i + -4iz + -1iz2 + 5z + 4z2 + z3 = 0

The solution to this equation could not be determined.

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