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

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


Simplifying
z2 + ((2i + -3) * z) + (5 + -1i) = 0

Reorder the terms:
z2 + ((-3 + 2i) * z) + (5 + -1i) = 0

Reorder the terms for easier multiplication:
z2 + (z(-3 + 2i)) + (5 + -1i) = 0
z2 + ((-3 * z + 2i * z)) + (5 + -1i) = 0

Reorder the terms:
z2 + ((2iz + -3z)) + (5 + -1i) = 0
z2 + ((2iz + -3z)) + (5 + -1i) = 0
z2 + (2iz + -3z) + (5 + -1i) = 0

Remove parenthesis around (2iz + -3z)
z2 + 2iz + -3z + (5 + -1i) = 0

Remove parenthesis around (5 + -1i)
z2 + 2iz + -3z + 5 + -1i = 0

Reorder the terms:
5 + -1i + 2iz + -3z + z2 = 0

Solving
5 + -1i + 2iz + -3z + z2 = 0

Solving for variable 'i'.

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

Add '-5' to each side of the equation.
5 + -1i + 2iz + -3z + -5 + z2 = 0 + -5

Reorder the terms:
5 + -5 + -1i + 2iz + -3z + z2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1i + 2iz + -3z + z2 = 0 + -5
-1i + 2iz + -3z + z2 = 0 + -5

Combine like terms: 0 + -5 = -5
-1i + 2iz + -3z + z2 = -5

Add '3z' to each side of the equation.
-1i + 2iz + -3z + 3z + z2 = -5 + 3z

Combine like terms: -3z + 3z = 0
-1i + 2iz + 0 + z2 = -5 + 3z
-1i + 2iz + z2 = -5 + 3z

Add '-1z2' to each side of the equation.
-1i + 2iz + z2 + -1z2 = -5 + 3z + -1z2

Combine like terms: z2 + -1z2 = 0
-1i + 2iz + 0 = -5 + 3z + -1z2
-1i + 2iz = -5 + 3z + -1z2

Reorder the terms:
5 + -1i + 2iz + -3z + z2 = -5 + 3z + -1z2 + 5 + -3z + z2

Reorder the terms:
5 + -1i + 2iz + -3z + z2 = -5 + 5 + 3z + -3z + -1z2 + z2

Combine like terms: -5 + 5 = 0
5 + -1i + 2iz + -3z + z2 = 0 + 3z + -3z + -1z2 + z2
5 + -1i + 2iz + -3z + z2 = 3z + -3z + -1z2 + z2

Combine like terms: 3z + -3z = 0
5 + -1i + 2iz + -3z + z2 = 0 + -1z2 + z2
5 + -1i + 2iz + -3z + z2 = -1z2 + z2

Combine like terms: -1z2 + z2 = 0
5 + -1i + 2iz + -3z + z2 = 0

The solution to this equation could not be determined.

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