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

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


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

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

Reorder the terms:
Z2 + (3iz + 2z) + 5 + -1i = 0
Z2 + (3iz + 2z) + 5 + -1i = 0

Reorder the terms:
5 + Z2 + -1i + 3iz + 2z = 0

Solving
5 + Z2 + -1i + 3iz + 2z = 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 + -1i + 3iz + -5 + 2z = 0 + -5

Reorder the terms:
5 + -5 + Z2 + -1i + 3iz + 2z = 0 + -5

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

The solution to this equation could not be determined.

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