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

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


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

Multiply (1 + -2z) * (2 + -3i)
(1(2 + -3i) + -2z * (2 + -3i)) = (3 + -1i) * z
((2 * 1 + -3i * 1) + -2z * (2 + -3i)) = (3 + -1i) * z
((2 + -3i) + -2z * (2 + -3i)) = (3 + -1i) * z
(2 + -3i + (2 * -2z + -3i * -2z)) = (3 + -1i) * z

Reorder the terms:
(2 + -3i + (6iz + -4z)) = (3 + -1i) * z
(2 + -3i + (6iz + -4z)) = (3 + -1i) * z
(2 + -3i + 6iz + -4z) = (3 + -1i) * z

Reorder the terms for easier multiplication:
2 + -3i + 6iz + -4z = z(3 + -1i)
2 + -3i + 6iz + -4z = (3 * z + -1i * z)

Reorder the terms:
2 + -3i + 6iz + -4z = (-1iz + 3z)
2 + -3i + 6iz + -4z = (-1iz + 3z)

Solving
2 + -3i + 6iz + -4z = -1iz + 3z

Solving for variable 'i'.

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

Add 'iz' to each side of the equation.
2 + -3i + 6iz + iz + -4z = -1iz + iz + 3z

Combine like terms: 6iz + iz = 7iz
2 + -3i + 7iz + -4z = -1iz + iz + 3z

Combine like terms: -1iz + iz = 0
2 + -3i + 7iz + -4z = 0 + 3z
2 + -3i + 7iz + -4z = 3z

Add '-2' to each side of the equation.
2 + -3i + 7iz + -2 + -4z = -2 + 3z

Reorder the terms:
2 + -2 + -3i + 7iz + -4z = -2 + 3z

Combine like terms: 2 + -2 = 0
0 + -3i + 7iz + -4z = -2 + 3z
-3i + 7iz + -4z = -2 + 3z

Add '4z' to each side of the equation.
-3i + 7iz + -4z + 4z = -2 + 3z + 4z

Combine like terms: -4z + 4z = 0
-3i + 7iz + 0 = -2 + 3z + 4z
-3i + 7iz = -2 + 3z + 4z

Combine like terms: 3z + 4z = 7z
-3i + 7iz = -2 + 7z

Reorder the terms:
2 + -3i + 7iz + -7z = -2 + 7z + 2 + -7z

Reorder the terms:
2 + -3i + 7iz + -7z = -2 + 2 + 7z + -7z

Combine like terms: -2 + 2 = 0
2 + -3i + 7iz + -7z = 0 + 7z + -7z
2 + -3i + 7iz + -7z = 7z + -7z

Combine like terms: 7z + -7z = 0
2 + -3i + 7iz + -7z = 0

The solution to this equation could not be determined.

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