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

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


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

Multiply (1 + -3i) * (5 + -2iz)
(1(5 + -2iz) + -3i * (5 + -2iz)) = (2i + -3)(3z + 2i)
((5 * 1 + -2iz * 1) + -3i * (5 + -2iz)) = (2i + -3)(3z + 2i)
((5 + -2iz) + -3i * (5 + -2iz)) = (2i + -3)(3z + 2i)
(5 + -2iz + (5 * -3i + -2iz * -3i)) = (2i + -3)(3z + 2i)
(5 + -2iz + (-15i + 6i2z)) = (2i + -3)(3z + 2i)

Reorder the terms:
(5 + -15i + -2iz + 6i2z) = (2i + -3)(3z + 2i)
(5 + -15i + -2iz + 6i2z) = (2i + -3)(3z + 2i)

Reorder the terms:
5 + -15i + -2iz + 6i2z = (-3 + 2i)(3z + 2i)

Reorder the terms:
5 + -15i + -2iz + 6i2z = (-3 + 2i)(2i + 3z)

Multiply (-3 + 2i) * (2i + 3z)
5 + -15i + -2iz + 6i2z = (-3(2i + 3z) + 2i * (2i + 3z))
5 + -15i + -2iz + 6i2z = ((2i * -3 + 3z * -3) + 2i * (2i + 3z))
5 + -15i + -2iz + 6i2z = ((-6i + -9z) + 2i * (2i + 3z))
5 + -15i + -2iz + 6i2z = (-6i + -9z + (2i * 2i + 3z * 2i))

Reorder the terms:
5 + -15i + -2iz + 6i2z = (-6i + -9z + (6iz + 4i2))
5 + -15i + -2iz + 6i2z = (-6i + -9z + (6iz + 4i2))

Reorder the terms:
5 + -15i + -2iz + 6i2z = (-6i + 6iz + 4i2 + -9z)
5 + -15i + -2iz + 6i2z = (-6i + 6iz + 4i2 + -9z)

Solving
5 + -15i + -2iz + 6i2z = -6i + 6iz + 4i2 + -9z

Solving for variable 'i'.

Reorder the terms:
5 + -15i + 6i + -2iz + -6iz + -4i2 + 6i2z + 9z = -6i + 6iz + 4i2 + -9z + 6i + -6iz + -4i2 + 9z

Combine like terms: -15i + 6i = -9i
5 + -9i + -2iz + -6iz + -4i2 + 6i2z + 9z = -6i + 6iz + 4i2 + -9z + 6i + -6iz + -4i2 + 9z

Combine like terms: -2iz + -6iz = -8iz
5 + -9i + -8iz + -4i2 + 6i2z + 9z = -6i + 6iz + 4i2 + -9z + 6i + -6iz + -4i2 + 9z

Reorder the terms:
5 + -9i + -8iz + -4i2 + 6i2z + 9z = -6i + 6i + 6iz + -6iz + 4i2 + -4i2 + -9z + 9z

Combine like terms: -6i + 6i = 0
5 + -9i + -8iz + -4i2 + 6i2z + 9z = 0 + 6iz + -6iz + 4i2 + -4i2 + -9z + 9z
5 + -9i + -8iz + -4i2 + 6i2z + 9z = 6iz + -6iz + 4i2 + -4i2 + -9z + 9z

Combine like terms: 6iz + -6iz = 0
5 + -9i + -8iz + -4i2 + 6i2z + 9z = 0 + 4i2 + -4i2 + -9z + 9z
5 + -9i + -8iz + -4i2 + 6i2z + 9z = 4i2 + -4i2 + -9z + 9z

Combine like terms: 4i2 + -4i2 = 0
5 + -9i + -8iz + -4i2 + 6i2z + 9z = 0 + -9z + 9z
5 + -9i + -8iz + -4i2 + 6i2z + 9z = -9z + 9z

Combine like terms: -9z + 9z = 0
5 + -9i + -8iz + -4i2 + 6i2z + 9z = 0

The solution to this equation could not be determined.

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