z^2-(1+2i)*z+3*(1+i)=0

Solution for z^2-(1+2i)*z+3*(1+i)=0 equation:

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

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

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

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

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

Solving for variable 'i'.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

The solution to this equation could not be determined.