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

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

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

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

Reorder the terms:
(-2iz2 + 1z2) + 2z + 1 = 0
(-2iz2 + 1z2) + 2z + 1 = 0

Reorder the terms:
1 + -2iz2 + 2z + 1z2 = 0

Solving
1 + -2iz2 + 2z + 1z2 = 0

Solving for variable 'i'.

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

Add '-1' to each side of the equation.
1 + -2iz2 + 2z + -1 + 1z2 = 0 + -1

Reorder the terms:
1 + -1 + -2iz2 + 2z + 1z2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2iz2 + 2z + 1z2 = 0 + -1
-2iz2 + 2z + 1z2 = 0 + -1

Combine like terms: 0 + -1 = -1
-2iz2 + 2z + 1z2 = -1

Add '-2z' to each side of the equation.
-2iz2 + 2z + -2z + 1z2 = -1 + -2z

Combine like terms: 2z + -2z = 0
-2iz2 + 0 + 1z2 = -1 + -2z
-2iz2 + 1z2 = -1 + -2z

Add '-1z2' to each side of the equation.
-2iz2 + 1z2 + -1z2 = -1 + -2z + -1z2

Combine like terms: 1z2 + -1z2 = 0
-2iz2 + 0 = -1 + -2z + -1z2
-2iz2 = -1 + -2z + -1z2

Divide each side by '-2z2'.
i = 0.5z-2 + z-1 + 0.5

Simplifying
i = 0.5z-2 + z-1 + 0.5

Reorder the terms:
i = 0.5 + 0.5z-2 + z-1