(-6+7i)+(14-6i)=0

Solution for (-6+7i)+(14-6i)=0 equation:

Simplifying
(-6 + 7i) + (14 + -6i) = 0

Remove parenthesis around (-6 + 7i)
-6 + 7i + (14 + -6i) = 0

Remove parenthesis around (14 + -6i)
-6 + 7i + 14 + -6i = 0

Reorder the terms:
-6 + 14 + 7i + -6i = 0

Combine like terms: -6 + 14 = 8
8 + 7i + -6i = 0

Combine like terms: 7i + -6i = 1i
8 + 1i = 0

Solving
8 + 1i = 0

Solving for variable 'i'.

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

Add '-8' to each side of the equation.
8 + -8 + 1i = 0 + -8

Combine like terms: 8 + -8 = 0
0 + 1i = 0 + -8
1i = 0 + -8

Combine like terms: 0 + -8 = -8
1i = -8

Divide each side by '1'.
i = -8

Simplifying
i = -8