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 + -1(5 + i) * z + (8 + i) = 0

Reorder the terms for easier multiplication:
z2 + -1z(5 + i) + (8 + i) = 0
z2 + (5 * -1z + i * -1z) + (8 + i) = 0

Reorder the terms:
z2 + (-1iz + -5z) + (8 + i) = 0
z2 + (-1iz + -5z) + (8 + i) = 0

Remove parenthesis around (8 + i)
z2 + -1iz + -5z + 8 + i = 0

Reorder the terms:
8 + i + -1iz + -5z + z2 = 0

Solving
8 + i + -1iz + -5z + z2 = 0

Solving for variable 'i'.

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

Add '-8' to each side of the equation.
8 + i + -1iz + -5z + -8 + z2 = 0 + -8

Reorder the terms:
8 + -8 + i + -1iz + -5z + z2 = 0 + -8

Combine like terms: 8 + -8 = 0
0 + i + -1iz + -5z + z2 = 0 + -8
i + -1iz + -5z + z2 = 0 + -8

Combine like terms: 0 + -8 = -8
i + -1iz + -5z + z2 = -8

Add '5z' to each side of the equation.
i + -1iz + -5z + 5z + z2 = -8 + 5z

Combine like terms: -5z + 5z = 0
i + -1iz + 0 + z2 = -8 + 5z
i + -1iz + z2 = -8 + 5z

Add '-1z2' to each side of the equation.
i + -1iz + z2 + -1z2 = -8 + 5z + -1z2

Combine like terms: z2 + -1z2 = 0
i + -1iz + 0 = -8 + 5z + -1z2
i + -1iz = -8 + 5z + -1z2

Reorder the terms:
8 + i + -1iz + -5z + z2 = -8 + 5z + -1z2 + 8 + -5z + z2

Reorder the terms:
8 + i + -1iz + -5z + z2 = -8 + 8 + 5z + -5z + -1z2 + z2

Combine like terms: -8 + 8 = 0
8 + i + -1iz + -5z + z2 = 0 + 5z + -5z + -1z2 + z2
8 + i + -1iz + -5z + z2 = 5z + -5z + -1z2 + z2

Combine like terms: 5z + -5z = 0
8 + i + -1iz + -5z + z2 = 0 + -1z2 + z2
8 + i + -1iz + -5z + z2 = -1z2 + z2

Combine like terms: -1z2 + z2 = 0
8 + i + -1iz + -5z + z2 = 0

The solution to this equation could not be determined.

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