z^2+(2+4i)z+(2-8i)=0

Solution for z^2+(2+4i)z+(2-8i)=0 equation:

Simplifying
z2 + (2 + 4i) * z + (2 + -8i) = 0

Reorder the terms for easier multiplication:
z2 + z(2 + 4i) + (2 + -8i) = 0
z2 + (2 * z + 4i * z) + (2 + -8i) = 0

Reorder the terms:
z2 + (4iz + 2z) + (2 + -8i) = 0
z2 + (4iz + 2z) + (2 + -8i) = 0

Remove parenthesis around (2 + -8i)
z2 + 4iz + 2z + 2 + -8i = 0

Reorder the terms:
2 + -8i + 4iz + 2z + z2 = 0

Solving
2 + -8i + 4iz + 2z + z2 = 0

Solving for variable 'i'.

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

Add '-2' to each side of the equation.
2 + -8i + 4iz + 2z + -2 + z2 = 0 + -2

Reorder the terms:
2 + -2 + -8i + 4iz + 2z + z2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -8i + 4iz + 2z + z2 = 0 + -2
-8i + 4iz + 2z + z2 = 0 + -2

Combine like terms: 0 + -2 = -2
-8i + 4iz + 2z + z2 = -2

Add '-2z' to each side of the equation.
-8i + 4iz + 2z + -2z + z2 = -2 + -2z

Combine like terms: 2z + -2z = 0
-8i + 4iz + 0 + z2 = -2 + -2z
-8i + 4iz + z2 = -2 + -2z

Add '-1z2' to each side of the equation.
-8i + 4iz + z2 + -1z2 = -2 + -2z + -1z2

Combine like terms: z2 + -1z2 = 0
-8i + 4iz + 0 = -2 + -2z + -1z2
-8i + 4iz = -2 + -2z + -1z2

Reorder the terms:
2 + -8i + 4iz + 2z + z2 = -2 + -2z + -1z2 + 2 + 2z + z2

Reorder the terms:
2 + -8i + 4iz + 2z + z2 = -2 + 2 + -2z + 2z + -1z2 + z2

Combine like terms: -2 + 2 = 0
2 + -8i + 4iz + 2z + z2 = 0 + -2z + 2z + -1z2 + z2
2 + -8i + 4iz + 2z + z2 = -2z + 2z + -1z2 + z2

Combine like terms: -2z + 2z = 0
2 + -8i + 4iz + 2z + z2 = 0 + -1z2 + z2
2 + -8i + 4iz + 2z + z2 = -1z2 + z2

Combine like terms: -1z2 + z2 = 0
2 + -8i + 4iz + 2z + z2 = 0

The solution to this equation could not be determined.