Z^2+(5+i)z+(8+i)=0

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Solution for Z^2+(5+i)z+(8+i)=0 equation: 


Simplifying
Z2 + (5 + i) * z + (8 + i) = 0

Reorder the terms for easier multiplication:
Z2 + z(5 + i) + (8 + i) = 0
Z2 + (5 * z + i * z) + (8 + i) = 0

Reorder the terms:
Z2 + (iz + 5z) + (8 + i) = 0
Z2 + (iz + 5z) + (8 + i) = 0

Remove parenthesis around (8 + i)
Z2 + iz + 5z + 8 + i = 0

Reorder the terms:
8 + Z2 + i + iz + 5z = 0

Solving
8 + Z2 + i + iz + 5z = 0

Solving for variable 'Z'.

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

Add '-8' to each side of the equation.
8 + Z2 + i + iz + -8 + 5z = 0 + -8

Reorder the terms:
8 + -8 + Z2 + i + iz + 5z = 0 + -8

Combine like terms: 8 + -8 = 0
0 + Z2 + i + iz + 5z = 0 + -8
Z2 + i + iz + 5z = 0 + -8

Combine like terms: 0 + -8 = -8
Z2 + i + iz + 5z = -8

Add '-1i' to each side of the equation.
Z2 + i + iz + -1i + 5z = -8 + -1i

Reorder the terms:
Z2 + i + -1i + iz + 5z = -8 + -1i

Combine like terms: i + -1i = 0
Z2 + 0 + iz + 5z = -8 + -1i
Z2 + iz + 5z = -8 + -1i

Add '-1iz' to each side of the equation.
Z2 + iz + -1iz + 5z = -8 + -1i + -1iz

Combine like terms: iz + -1iz = 0
Z2 + 0 + 5z = -8 + -1i + -1iz
Z2 + 5z = -8 + -1i + -1iz

Add '-5z' to each side of the equation.
Z2 + 5z + -5z = -8 + -1i + -1iz + -5z

Combine like terms: 5z + -5z = 0
Z2 + 0 = -8 + -1i + -1iz + -5z
Z2 = -8 + -1i + -1iz + -5z

Simplifying
Z2 = -8 + -1i + -1iz + -5z

Reorder the terms:
8 + Z2 + i + iz + 5z = -8 + -1i + -1iz + -5z + 8 + i + iz + 5z

Reorder the terms:
8 + Z2 + i + iz + 5z = -8 + 8 + -1i + i + -1iz + iz + -5z + 5z

Combine like terms: -8 + 8 = 0
8 + Z2 + i + iz + 5z = 0 + -1i + i + -1iz + iz + -5z + 5z
8 + Z2 + i + iz + 5z = -1i + i + -1iz + iz + -5z + 5z

Combine like terms: -1i + i = 0
8 + Z2 + i + iz + 5z = 0 + -1iz + iz + -5z + 5z
8 + Z2 + i + iz + 5z = -1iz + iz + -5z + 5z

Combine like terms: -1iz + iz = 0
8 + Z2 + i + iz + 5z = 0 + -5z + 5z
8 + Z2 + i + iz + 5z = -5z + 5z

Combine like terms: -5z + 5z = 0
8 + Z2 + i + iz + 5z = 0

The solution to this equation could not be determined.

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