(z+z)+i(z-z)=2i-6

Solution for (z+z)+i(z-z)=2i-6 equation:

Simplifying
(z + z) + i(z + -1z) = 2i + -6

Combine like terms: z + z = 2z
(2z) + i(z + -1z) = 2i + -6
(2z) + i(z + -1z) = 2i + -6

Combine like terms: z + -1z = 0
(2z) + i(0) = 2i + -6

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

Anything times zero is zero.
(2z) + 0i = 2i + -6

Reorder the terms:
0 + (2z) = 2i + -6
Remove the zero:
(2z) = 2i + -6

Reorder the terms:
(2z) = -6 + 2i

Solving
(2z) = -6 + 2i

Solving for variable 'z'.

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

Divide each side by '2'.
z = -3 + i

Simplifying
z = -3 + i