-2+3i+12i=9i-(2-di)

Solution for -2+3i+12i=9i-(2-di) equation:

Simplifying
-2 + 3i + 12i = 9i + -1(2 + -1di)

Combine like terms: 3i + 12i = 15i
-2 + 15i = 9i + -1(2 + -1di)
-2 + 15i = 9i + (2 * -1 + -1di * -1)
-2 + 15i = 9i + (-2 + 1di)

Reorder the terms:
-2 + 15i = -2 + 1di + 9i

Add '2' to each side of the equation.
-2 + 2 + 15i = -2 + 1di + 2 + 9i

Combine like terms: -2 + 2 = 0
0 + 15i = -2 + 1di + 2 + 9i
15i = -2 + 1di + 2 + 9i

Reorder the terms:
15i = -2 + 2 + 1di + 9i

Combine like terms: -2 + 2 = 0
15i = 0 + 1di + 9i
15i = 1di + 9i

Solving
15i = 1di + 9i

Solving for variable 'i'.

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

Add '-1di' to each side of the equation.
-1di + 15i = 1di + -1di + 9i

Combine like terms: 1di + -1di = 0
-1di + 15i = 0 + 9i
-1di + 15i = 9i

Add '-9i' to each side of the equation.
-1di + 15i + -9i = 9i + -9i

Combine like terms: 15i + -9i = 6i
-1di + 6i = 9i + -9i

Combine like terms: 9i + -9i = 0
-1di + 6i = 0

Factor out the Greatest Common Factor (GCF), 'i'.
i(-1d + 6) = 0

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 '(-1d + 6)' equal to zero and attempt to solve:

Simplifying
-1d + 6 = 0

Reorder the terms:
6 + -1d = 0

Solving
6 + -1d = 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 + -1d = 0 + -6

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

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

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

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

Simplifying
0 = -6 + d

The solution to this equation could not be determined.

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