z^2+(2+5i)z+5i=0

Solution for z^2+(2+5i)z+5i=0 equation:

Simplifying
z2 + (2 + 5i) * z + 5i = 0

Reorder the terms for easier multiplication:
z2 + z(2 + 5i) + 5i = 0
z2 + (2 * z + 5i * z) + 5i = 0

Reorder the terms:
z2 + (5iz + 2z) + 5i = 0
z2 + (5iz + 2z) + 5i = 0

Reorder the terms:
5i + 5iz + 2z + z2 = 0

Solving
5i + 5iz + 2z + z2 = 0

Solving for variable 'i'.

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

Add '-2z' to each side of the equation.
5i + 5iz + 2z + -2z + z2 = 0 + -2z

Combine like terms: 2z + -2z = 0
5i + 5iz + 0 + z2 = 0 + -2z
5i + 5iz + z2 = 0 + -2z
Remove the zero:
5i + 5iz + z2 = -2z

Add '-1z2' to each side of the equation.
5i + 5iz + z2 + -1z2 = -2z + -1z2

Combine like terms: z2 + -1z2 = 0
5i + 5iz + 0 = -2z + -1z2
5i + 5iz = -2z + -1z2

Reorder the terms:
5i + 5iz + 2z + z2 = -2z + 2z + -1z2 + z2

Combine like terms: -2z + 2z = 0
5i + 5iz + 2z + z2 = 0 + -1z2 + z2
5i + 5iz + 2z + z2 = -1z2 + z2

Combine like terms: -1z2 + z2 = 0
5i + 5iz + 2z + z2 = 0

The solution to this equation could not be determined.