(3+2i)+(4+xi)=7-5i

Solution for (3+2i)+(4+xi)=7-5i equation:

Simplifying
(3 + 2i) + (4 + xi) = 7 + -5i

Remove parenthesis around (3 + 2i)
3 + 2i + (4 + xi) = 7 + -5i

Remove parenthesis around (4 + ix)
3 + 2i + 4 + ix = 7 + -5i

Reorder the terms:
3 + 4 + 2i + ix = 7 + -5i

Combine like terms: 3 + 4 = 7
7 + 2i + ix = 7 + -5i

Add '-7' to each side of the equation.
7 + 2i + -7 + ix = 7 + -7 + -5i

Reorder the terms:
7 + -7 + 2i + ix = 7 + -7 + -5i

Combine like terms: 7 + -7 = 0
0 + 2i + ix = 7 + -7 + -5i
2i + ix = 7 + -7 + -5i

Combine like terms: 7 + -7 = 0
2i + ix = 0 + -5i
2i + ix = -5i

Solving
2i + ix = -5i

Solving for variable 'i'.

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

Add '5i' to each side of the equation.
2i + 5i + ix = -5i + 5i

Combine like terms: 2i + 5i = 7i
7i + ix = -5i + 5i

Combine like terms: -5i + 5i = 0
7i + ix = 0

Factor out the Greatest Common Factor (GCF), 'i'.
i(7 + x) = 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 '(7 + x)' equal to zero and attempt to solve:

Simplifying
7 + x = 0

Solving
7 + x = 0

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

Add '-7' to each side of the equation.
7 + -7 + x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + x = 0 + -7
x = 0 + -7

Combine like terms: 0 + -7 = -7
x = -7

Add '-1x' to each side of the equation.
x + -1x = -7 + -1x

Combine like terms: x + -1x = 0
0 = -7 + -1x

Simplifying
0 = -7 + -1x

The solution to this equation could not be determined.

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