((2+3i)-(3-2i))+(6+i)=

Solution for ((2+3i)-(3-2i))+(6+i)= equation:

Simplifying
((2 + 3i) + -1(3 + -2i)) + (6 + i) = 0

Remove parenthesis around (2 + 3i)
(2 + 3i + -1(3 + -2i)) + (6 + i) = 0
(2 + 3i + (3 * -1 + -2i * -1)) + (6 + i) = 0
(2 + 3i + (-3 + 2i)) + (6 + i) = 0

Reorder the terms:
(2 + -3 + 3i + 2i) + (6 + i) = 0

Combine like terms: 2 + -3 = -1
(-1 + 3i + 2i) + (6 + i) = 0

Combine like terms: 3i + 2i = 5i
(-1 + 5i) + (6 + i) = 0

Remove parenthesis around (-1 + 5i)
-1 + 5i + (6 + i) = 0

Remove parenthesis around (6 + i)
-1 + 5i + 6 + i = 0

Reorder the terms:
-1 + 6 + 5i + i = 0

Combine like terms: -1 + 6 = 5
5 + 5i + i = 0

Combine like terms: 5i + i = 6i
5 + 6i = 0

Solving
5 + 6i = 0

Solving for variable 'i'.

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

Add '-5' to each side of the equation.
5 + -5 + 6i = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 6i = 0 + -5
6i = 0 + -5

Combine like terms: 0 + -5 = -5
6i = -5

Divide each side by '6'.
i = -0.8333333333

Simplifying
i = -0.8333333333