z^2+6z-3+I*(4*z+6)=0

Solution for z^2+6z-3+I*(4*z+6)=0 equation:

Simplifying
z2 + 6z + -3 + I(4z + 6) = 0

Reorder the terms:
z2 + 6z + -3 + I(6 + 4z) = 0
z2 + 6z + -3 + (6 * I + 4z * I) = 0
z2 + 6z + -3 + (6I + 4zI) = 0

Reorder the terms:
-3 + 6I + 6z + 4zI + z2 = 0

Solving
-3 + 6I + 6z + 4zI + z2 = 0

Solving for variable 'I'.

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

Add '3' to each side of the equation.
-3 + 6I + 6z + 4zI + 3 + z2 = 0 + 3

Reorder the terms:
-3 + 3 + 6I + 6z + 4zI + z2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + 6I + 6z + 4zI + z2 = 0 + 3
6I + 6z + 4zI + z2 = 0 + 3

Combine like terms: 0 + 3 = 3
6I + 6z + 4zI + z2 = 3

Add '-6z' to each side of the equation.
6I + 6z + 4zI + -6z + z2 = 3 + -6z

Reorder the terms:
6I + 6z + -6z + 4zI + z2 = 3 + -6z

Combine like terms: 6z + -6z = 0
6I + 0 + 4zI + z2 = 3 + -6z
6I + 4zI + z2 = 3 + -6z

Add '-1z2' to each side of the equation.
6I + 4zI + z2 + -1z2 = 3 + -6z + -1z2

Combine like terms: z2 + -1z2 = 0
6I + 4zI + 0 = 3 + -6z + -1z2
6I + 4zI = 3 + -6z + -1z2

Reorder the terms:
-3 + 6I + 6z + 4zI + z2 = 3 + -6z + -1z2 + -3 + 6z + z2

Reorder the terms:
-3 + 6I + 6z + 4zI + z2 = 3 + -3 + -6z + 6z + -1z2 + z2

Combine like terms: 3 + -3 = 0
-3 + 6I + 6z + 4zI + z2 = 0 + -6z + 6z + -1z2 + z2
-3 + 6I + 6z + 4zI + z2 = -6z + 6z + -1z2 + z2

Combine like terms: -6z + 6z = 0
-3 + 6I + 6z + 4zI + z2 = 0 + -1z2 + z2
-3 + 6I + 6z + 4zI + z2 = -1z2 + z2

Combine like terms: -1z2 + z2 = 0
-3 + 6I + 6z + 4zI + z2 = 0

The solution to this equation could not be determined.