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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

The solution to this equation could not be determined.