z^2-(4+i)z+(6+2i)=0

Solution for z^2-(4+i)z+(6+2i)=0 equation:

Simplifying
z2 + -1(4 + i) * z + (6 + 2i) = 0

Reorder the terms for easier multiplication:
z2 + -1z(4 + i) + (6 + 2i) = 0
z2 + (4 * -1z + i * -1z) + (6 + 2i) = 0

Reorder the terms:
z2 + (-1iz + -4z) + (6 + 2i) = 0
z2 + (-1iz + -4z) + (6 + 2i) = 0

Remove parenthesis around (6 + 2i)
z2 + -1iz + -4z + 6 + 2i = 0

Reorder the terms:
6 + 2i + -1iz + -4z + z2 = 0

Solving
6 + 2i + -1iz + -4z + z2 = 0

Solving for variable 'i'.

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

Add '-6' to each side of the equation.
6 + 2i + -1iz + -4z + -6 + z2 = 0 + -6

Reorder the terms:
6 + -6 + 2i + -1iz + -4z + z2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + 2i + -1iz + -4z + z2 = 0 + -6
2i + -1iz + -4z + z2 = 0 + -6

Combine like terms: 0 + -6 = -6
2i + -1iz + -4z + z2 = -6

Add '4z' to each side of the equation.
2i + -1iz + -4z + 4z + z2 = -6 + 4z

Combine like terms: -4z + 4z = 0
2i + -1iz + 0 + z2 = -6 + 4z
2i + -1iz + z2 = -6 + 4z

Add '-1z2' to each side of the equation.
2i + -1iz + z2 + -1z2 = -6 + 4z + -1z2

Combine like terms: z2 + -1z2 = 0
2i + -1iz + 0 = -6 + 4z + -1z2
2i + -1iz = -6 + 4z + -1z2

Reorder the terms:
6 + 2i + -1iz + -4z + z2 = -6 + 4z + -1z2 + 6 + -4z + z2

Reorder the terms:
6 + 2i + -1iz + -4z + z2 = -6 + 6 + 4z + -4z + -1z2 + z2

Combine like terms: -6 + 6 = 0
6 + 2i + -1iz + -4z + z2 = 0 + 4z + -4z + -1z2 + z2
6 + 2i + -1iz + -4z + z2 = 4z + -4z + -1z2 + z2

Combine like terms: 4z + -4z = 0
6 + 2i + -1iz + -4z + z2 = 0 + -1z2 + z2
6 + 2i + -1iz + -4z + z2 = -1z2 + z2

Combine like terms: -1z2 + z2 = 0
6 + 2i + -1iz + -4z + z2 = 0

The solution to this equation could not be determined.