3(2+iy)=8-12i-(2-iy)

Solution for 3(2+iy)=8-12i-(2-iy) equation:

Simplifying
3(2 + iy) = 8 + -12i + -1(2 + -1iy)
(2 * 3 + iy * 3) = 8 + -12i + -1(2 + -1iy)
(6 + 3iy) = 8 + -12i + -1(2 + -1iy)
6 + 3iy = 8 + -12i + (2 * -1 + -1iy * -1)
6 + 3iy = 8 + -12i + (-2 + 1iy)

Reorder the terms:
6 + 3iy = 8 + -2 + -12i + 1iy

Combine like terms: 8 + -2 = 6
6 + 3iy = 6 + -12i + 1iy

Add '-6' to each side of the equation.
6 + -6 + 3iy = 6 + -12i + -6 + 1iy

Combine like terms: 6 + -6 = 0
0 + 3iy = 6 + -12i + -6 + 1iy
3iy = 6 + -12i + -6 + 1iy

Reorder the terms:
3iy = 6 + -6 + -12i + 1iy

Combine like terms: 6 + -6 = 0
3iy = 0 + -12i + 1iy
3iy = -12i + 1iy

Solving
3iy = -12i + 1iy

Solving for variable 'i'.

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

Add '12i' to each side of the equation.
12i + 3iy = -12i + 12i + 1iy

Combine like terms: -12i + 12i = 0
12i + 3iy = 0 + 1iy
12i + 3iy = 1iy

Add '-1iy' to each side of the equation.
12i + 3iy + -1iy = 1iy + -1iy

Combine like terms: 3iy + -1iy = 2iy
12i + 2iy = 1iy + -1iy

Combine like terms: 1iy + -1iy = 0
12i + 2iy = 0

Factor out the Greatest Common Factor (GCF), '2i'.
2i(6 + y) = 0

Ignore the factor 2.
Subproblem 1
Set the factor 'i' equal to zero and attempt to solve:

Simplifying
i = 0

Solving
i = 0

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

Simplifying
i = 0
Subproblem 2
Set the factor '(6 + y)' equal to zero and attempt to solve:

Simplifying
6 + y = 0

Solving
6 + y = 0

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

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

Combine like terms: 6 + -6 = 0
0 + y = 0 + -6
y = 0 + -6

Combine like terms: 0 + -6 = -6
y = -6

Add '-1y' to each side of the equation.
y + -1y = -6 + -1y

Combine like terms: y + -1y = 0
0 = -6 + -1y

Simplifying
0 = -6 + -1y

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
i = {0}