(5+2i)z+(3+2i)=(2-i)-(1+i)z

Solution for (5+2i)z+(3+2i)=(2-i)-(1+i)z equation:

Simplifying
(5 + 2i) * z + (3 + 2i) = (2 + -1i) + -1(1 + i) * z

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

Reorder the terms:
(2iz + 5z) + (3 + 2i) = (2 + -1i) + -1(1 + i) * z
(2iz + 5z) + (3 + 2i) = (2 + -1i) + -1(1 + i) * z

Remove parenthesis around (3 + 2i)
2iz + 5z + 3 + 2i = (2 + -1i) + -1(1 + i) * z

Reorder the terms:
3 + 2i + 2iz + 5z = (2 + -1i) + -1(1 + i) * z

Remove parenthesis around (2 + -1i)
3 + 2i + 2iz + 5z = 2 + -1i + -1(1 + i) * z

Reorder the terms for easier multiplication:
3 + 2i + 2iz + 5z = 2 + -1i + -1z(1 + i)
3 + 2i + 2iz + 5z = 2 + -1i + (1 * -1z + i * -1z)

Reorder the terms:
3 + 2i + 2iz + 5z = 2 + -1i + (-1iz + -1z)
3 + 2i + 2iz + 5z = 2 + -1i + (-1iz + -1z)

Solving
3 + 2i + 2iz + 5z = 2 + -1i + -1iz + -1z

Solving for variable 'i'.

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

Add 'i' to each side of the equation.
3 + 2i + 2iz + i + 5z = 2 + -1i + -1iz + i + -1z

Reorder the terms:
3 + 2i + i + 2iz + 5z = 2 + -1i + -1iz + i + -1z

Combine like terms: 2i + i = 3i
3 + 3i + 2iz + 5z = 2 + -1i + -1iz + i + -1z

Reorder the terms:
3 + 3i + 2iz + 5z = 2 + -1i + i + -1iz + -1z

Combine like terms: -1i + i = 0
3 + 3i + 2iz + 5z = 2 + 0 + -1iz + -1z
3 + 3i + 2iz + 5z = 2 + -1iz + -1z

Add 'iz' to each side of the equation.
3 + 3i + 2iz + iz + 5z = 2 + -1iz + iz + -1z

Combine like terms: 2iz + iz = 3iz
3 + 3i + 3iz + 5z = 2 + -1iz + iz + -1z

Combine like terms: -1iz + iz = 0
3 + 3i + 3iz + 5z = 2 + 0 + -1z
3 + 3i + 3iz + 5z = 2 + -1z

Add '-3' to each side of the equation.
3 + 3i + 3iz + -3 + 5z = 2 + -3 + -1z

Reorder the terms:
3 + -3 + 3i + 3iz + 5z = 2 + -3 + -1z

Combine like terms: 3 + -3 = 0
0 + 3i + 3iz + 5z = 2 + -3 + -1z
3i + 3iz + 5z = 2 + -3 + -1z

Combine like terms: 2 + -3 = -1
3i + 3iz + 5z = -1 + -1z

Add '-5z' to each side of the equation.
3i + 3iz + 5z + -5z = -1 + -1z + -5z

Combine like terms: 5z + -5z = 0
3i + 3iz + 0 = -1 + -1z + -5z
3i + 3iz = -1 + -1z + -5z

Combine like terms: -1z + -5z = -6z
3i + 3iz = -1 + -6z

Reorder the terms:
1 + 3i + 3iz + 6z = -1 + -6z + 1 + 6z

Reorder the terms:
1 + 3i + 3iz + 6z = -1 + 1 + -6z + 6z

Combine like terms: -1 + 1 = 0
1 + 3i + 3iz + 6z = 0 + -6z + 6z
1 + 3i + 3iz + 6z = -6z + 6z

Combine like terms: -6z + 6z = 0
1 + 3i + 3iz + 6z = 0

The solution to this equation could not be determined.