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

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


Simplifying
Z2 + -1(3 + 2i) * z + 5 + i = 0

Reorder the terms for easier multiplication:
Z2 + -1z(3 + 2i) + 5 + i = 0
Z2 + (3 * -1z + 2i * -1z) + 5 + i = 0

Reorder the terms:
Z2 + (-2iz + -3z) + 5 + i = 0
Z2 + (-2iz + -3z) + 5 + i = 0

Reorder the terms:
5 + Z2 + i + -2iz + -3z = 0

Solving
5 + Z2 + i + -2iz + -3z = 0

Solving for variable 'Z'.

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

Add '-5' to each side of the equation.
5 + Z2 + i + -2iz + -5 + -3z = 0 + -5

Reorder the terms:
5 + -5 + Z2 + i + -2iz + -3z = 0 + -5

Combine like terms: 5 + -5 = 0
0 + Z2 + i + -2iz + -3z = 0 + -5
Z2 + i + -2iz + -3z = 0 + -5

Combine like terms: 0 + -5 = -5
Z2 + i + -2iz + -3z = -5

Add '-1i' to each side of the equation.
Z2 + i + -2iz + -1i + -3z = -5 + -1i

Reorder the terms:
Z2 + i + -1i + -2iz + -3z = -5 + -1i

Combine like terms: i + -1i = 0
Z2 + 0 + -2iz + -3z = -5 + -1i
Z2 + -2iz + -3z = -5 + -1i

Add '2iz' to each side of the equation.
Z2 + -2iz + 2iz + -3z = -5 + -1i + 2iz

Combine like terms: -2iz + 2iz = 0
Z2 + 0 + -3z = -5 + -1i + 2iz
Z2 + -3z = -5 + -1i + 2iz

Add '3z' to each side of the equation.
Z2 + -3z + 3z = -5 + -1i + 2iz + 3z

Combine like terms: -3z + 3z = 0
Z2 + 0 = -5 + -1i + 2iz + 3z
Z2 = -5 + -1i + 2iz + 3z

Simplifying
Z2 = -5 + -1i + 2iz + 3z

Reorder the terms:
5 + Z2 + i + -2iz + -3z = -5 + -1i + 2iz + 3z + 5 + i + -2iz + -3z

Reorder the terms:
5 + Z2 + i + -2iz + -3z = -5 + 5 + -1i + i + 2iz + -2iz + 3z + -3z

Combine like terms: -5 + 5 = 0
5 + Z2 + i + -2iz + -3z = 0 + -1i + i + 2iz + -2iz + 3z + -3z
5 + Z2 + i + -2iz + -3z = -1i + i + 2iz + -2iz + 3z + -3z

Combine like terms: -1i + i = 0
5 + Z2 + i + -2iz + -3z = 0 + 2iz + -2iz + 3z + -3z
5 + Z2 + i + -2iz + -3z = 2iz + -2iz + 3z + -3z

Combine like terms: 2iz + -2iz = 0
5 + Z2 + i + -2iz + -3z = 0 + 3z + -3z
5 + Z2 + i + -2iz + -3z = 3z + -3z

Combine like terms: 3z + -3z = 0
5 + Z2 + i + -2iz + -3z = 0

The solution to this equation could not be determined.

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