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

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


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

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

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

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

Reorder the terms:
-1i + iz2 + -1m + -3z + 3z2 + z3 = 0

Solving
-1i + iz2 + -1m + -3z + 3z2 + z3 = 0

Solving for variable 'i'.

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

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

Reorder the terms:
-1i + iz2 + -1m + m + -3z + 3z2 + z3 = 0 + m

Combine like terms: -1m + m = 0
-1i + iz2 + 0 + -3z + 3z2 + z3 = 0 + m
-1i + iz2 + -3z + 3z2 + z3 = 0 + m
Remove the zero:
-1i + iz2 + -3z + 3z2 + z3 = m

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

Reorder the terms:
-1i + iz2 + -3z + 3z + 3z2 + z3 = m + 3z

Combine like terms: -3z + 3z = 0
-1i + iz2 + 0 + 3z2 + z3 = m + 3z
-1i + iz2 + 3z2 + z3 = m + 3z

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

Combine like terms: 3z2 + -3z2 = 0
-1i + iz2 + 0 + z3 = m + 3z + -3z2
-1i + iz2 + z3 = m + 3z + -3z2

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

Combine like terms: z3 + -1z3 = 0
-1i + iz2 + 0 = m + 3z + -3z2 + -1z3
-1i + iz2 = m + 3z + -3z2 + -1z3

Reorder the terms:
-1i + iz2 + -1m + -3z + 3z2 + z3 = m + -1m + 3z + -3z + -3z2 + 3z2 + -1z3 + z3

Combine like terms: m + -1m = 0
-1i + iz2 + -1m + -3z + 3z2 + z3 = 0 + 3z + -3z + -3z2 + 3z2 + -1z3 + z3
-1i + iz2 + -1m + -3z + 3z2 + z3 = 3z + -3z + -3z2 + 3z2 + -1z3 + z3

Combine like terms: 3z + -3z = 0
-1i + iz2 + -1m + -3z + 3z2 + z3 = 0 + -3z2 + 3z2 + -1z3 + z3
-1i + iz2 + -1m + -3z + 3z2 + z3 = -3z2 + 3z2 + -1z3 + z3

Combine like terms: -3z2 + 3z2 = 0
-1i + iz2 + -1m + -3z + 3z2 + z3 = 0 + -1z3 + z3
-1i + iz2 + -1m + -3z + 3z2 + z3 = -1z3 + z3

Combine like terms: -1z3 + z3 = 0
-1i + iz2 + -1m + -3z + 3z2 + z3 = 0

The solution to this equation could not be determined.

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