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

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

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

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

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

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

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

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

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

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

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

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

Divide each side by '4'.
i = -0.5 + -0.5z + -0.25z2

Simplifying
i = -0.5 + -0.5z + -0.25z2