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

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

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

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

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

Remove parenthesis around (-1 + 3i)
z2 + 3iz + 2z + -1 + 3i = 0

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

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

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

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

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

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

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

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

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

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

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

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

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

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

The solution to this equation could not be determined.