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

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

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

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

Remove parenthesis around (-1z)
0 + i(z + -1 * -1z) = 2i + -6

Multiply -1 * -1
0 + i(z + 1z) = 2i + -6

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

Remove parenthesis around (2z)
0 + i * 2z = 2i + -6

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

Multiply i * z
0 + 2iz = 2i + -6
Remove the zero:
2iz = 2i + -6

Reorder the terms:
2iz = -6 + 2i

Solving
2iz = -6 + 2i

Solving for variable 'i'.

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

Add '-2i' to each side of the equation.
-2i + 2iz = -6 + 2i + -2i

Combine like terms: 2i + -2i = 0
-2i + 2iz = -6 + 0
-2i + 2iz = -6

Reorder the terms:
6 + -2i + 2iz = -6 + 6

Combine like terms: -6 + 6 = 0
6 + -2i + 2iz = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + -1i + iz) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(3 + -1i + iz)' equal to zero and attempt to solve:

Simplifying
3 + -1i + iz = 0

Solving
3 + -1i + iz = 0

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

Add '-3' to each side of the equation.
3 + -1i + -3 + iz = 0 + -3

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

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

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

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.