(1+2i)x+3-2i=4-5i+3ix

Solution for (1+2i)x+3-2i=4-5i+3ix equation:

Simplifying
(1 + 2i) * x + 3 + -2i = 4 + -5i + 3ix

Reorder the terms for easier multiplication:
x(1 + 2i) + 3 + -2i = 4 + -5i + 3ix
(1 * x + 2i * x) + 3 + -2i = 4 + -5i + 3ix

Reorder the terms:
(2ix + 1x) + 3 + -2i = 4 + -5i + 3ix
(2ix + 1x) + 3 + -2i = 4 + -5i + 3ix

Reorder the terms:
3 + -2i + 2ix + 1x = 4 + -5i + 3ix

Solving
3 + -2i + 2ix + 1x = 4 + -5i + 3ix

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.
3 + -2i + 2ix + 5i + 1x = 4 + -5i + 5i + 3ix

Reorder the terms:
3 + -2i + 5i + 2ix + 1x = 4 + -5i + 5i + 3ix

Combine like terms: -2i + 5i = 3i
3 + 3i + 2ix + 1x = 4 + -5i + 5i + 3ix

Combine like terms: -5i + 5i = 0
3 + 3i + 2ix + 1x = 4 + 0 + 3ix
3 + 3i + 2ix + 1x = 4 + 3ix

Add '-3ix' to each side of the equation.
3 + 3i + 2ix + -3ix + 1x = 4 + 3ix + -3ix

Combine like terms: 2ix + -3ix = -1ix
3 + 3i + -1ix + 1x = 4 + 3ix + -3ix

Combine like terms: 3ix + -3ix = 0
3 + 3i + -1ix + 1x = 4 + 0
3 + 3i + -1ix + 1x = 4

Add '-3' to each side of the equation.
3 + 3i + -1ix + -3 + 1x = 4 + -3

Reorder the terms:
3 + -3 + 3i + -1ix + 1x = 4 + -3

Combine like terms: 3 + -3 = 0
0 + 3i + -1ix + 1x = 4 + -3
3i + -1ix + 1x = 4 + -3

Combine like terms: 4 + -3 = 1
3i + -1ix + 1x = 1

Add '-1x' to each side of the equation.
3i + -1ix + 1x + -1x = 1 + -1x

Combine like terms: 1x + -1x = 0
3i + -1ix + 0 = 1 + -1x
3i + -1ix = 1 + -1x

Reorder the terms:
-1 + 3i + -1ix + x = 1 + -1x + -1 + x

Reorder the terms:
-1 + 3i + -1ix + x = 1 + -1 + -1x + x

Combine like terms: 1 + -1 = 0
-1 + 3i + -1ix + x = 0 + -1x + x
-1 + 3i + -1ix + x = -1x + x

Combine like terms: -1x + x = 0
-1 + 3i + -1ix + x = 0

The solution to this equation could not be determined.