(x^2+6)+(2xi)=0

Solution for (x^2+6)+(2xi)=0 equation:

Simplifying
(x2 + 6) + (2xi) = 0

Reorder the terms:
(6 + x2) + (2xi) = 0

Remove parenthesis around (6 + x2)
6 + x2 + (2xi) = 0

Reorder the terms:
6 + (2ix) + x2 = 0

Solving
6 + (2ix) + x2 = 0

Solving for variable 'i'.

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

Add '-6' to each side of the equation.
6 + (2ix) + -6 + x2 = 0 + -6

Reorder the terms:
6 + -6 + (2ix) + x2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + (2ix) + x2 = 0 + -6
(2ix) + x2 = 0 + -6

Combine like terms: 0 + -6 = -6
(2ix) + x2 = -6

Add '-1x2' to each side of the equation.
(2ix) + x2 + -1x2 = -6 + -1x2

Combine like terms: x2 + -1x2 = 0
(2ix) + 0 = -6 + -1x2
(2ix) = -6 + -1x2

Divide each side by '(2x)'.
i = -3x-1 + -0.5x

Simplifying
i = -3x-1 + -0.5x