z^2+(3+2i)z+6i=0

Solution for z^2+(3+2i)z+6i=0 equation:

Simplifying
z2 + (3 + 2i) * z + 6i = 0

Reorder the terms for easier multiplication:
z2 + z(3 + 2i) + 6i = 0
z2 + (3 * z + 2i * z) + 6i = 0

Reorder the terms:
z2 + (2iz + 3z) + 6i = 0
z2 + (2iz + 3z) + 6i = 0

Reorder the terms:
6i + 2iz + 3z + z2 = 0

Solving
6i + 2iz + 3z + z2 = 0

Solving for variable 'i'.

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

Add '-3z' to each side of the equation.
6i + 2iz + 3z + -3z + z2 = 0 + -3z

Combine like terms: 3z + -3z = 0
6i + 2iz + 0 + z2 = 0 + -3z
6i + 2iz + z2 = 0 + -3z
Remove the zero:
6i + 2iz + z2 = -3z

Add '-1z2' to each side of the equation.
6i + 2iz + z2 + -1z2 = -3z + -1z2

Combine like terms: z2 + -1z2 = 0
6i + 2iz + 0 = -3z + -1z2
6i + 2iz = -3z + -1z2

Reorder the terms:
6i + 2iz + 3z + z2 = -3z + 3z + -1z2 + z2

Combine like terms: -3z + 3z = 0
6i + 2iz + 3z + z2 = 0 + -1z2 + z2
6i + 2iz + 3z + z2 = -1z2 + z2

Combine like terms: -1z2 + z2 = 0
6i + 2iz + 3z + z2 = 0

The solution to this equation could not be determined.