(z-3-2i)(z+8i)=(z+3i)(z+2)

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Solution for (z-3-2i)(z+8i)=(z+3i)(z+2) equation: 


Simplifying
(z + -3 + -2i)(z + 8i) = (z + 3i)(z + 2)

Reorder the terms:
(-3 + -2i + z)(z + 8i) = (z + 3i)(z + 2)

Reorder the terms:
(-3 + -2i + z)(8i + z) = (z + 3i)(z + 2)

Multiply (-3 + -2i + z) * (8i + z)
(-3(8i + z) + -2i * (8i + z) + z(8i + z)) = (z + 3i)(z + 2)
((8i * -3 + z * -3) + -2i * (8i + z) + z(8i + z)) = (z + 3i)(z + 2)
((-24i + -3z) + -2i * (8i + z) + z(8i + z)) = (z + 3i)(z + 2)
(-24i + -3z + (8i * -2i + z * -2i) + z(8i + z)) = (z + 3i)(z + 2)

Reorder the terms:
(-24i + -3z + (-2iz + -16i2) + z(8i + z)) = (z + 3i)(z + 2)
(-24i + -3z + (-2iz + -16i2) + z(8i + z)) = (z + 3i)(z + 2)
(-24i + -3z + -2iz + -16i2 + (8i * z + z * z)) = (z + 3i)(z + 2)
(-24i + -3z + -2iz + -16i2 + (8iz + z2)) = (z + 3i)(z + 2)

Reorder the terms:
(-24i + -2iz + 8iz + -16i2 + -3z + z2) = (z + 3i)(z + 2)

Combine like terms: -2iz + 8iz = 6iz
(-24i + 6iz + -16i2 + -3z + z2) = (z + 3i)(z + 2)

Reorder the terms:
-24i + 6iz + -16i2 + -3z + z2 = (3i + z)(z + 2)

Reorder the terms:
-24i + 6iz + -16i2 + -3z + z2 = (3i + z)(2 + z)

Multiply (3i + z) * (2 + z)
-24i + 6iz + -16i2 + -3z + z2 = (3i * (2 + z) + z(2 + z))
-24i + 6iz + -16i2 + -3z + z2 = ((2 * 3i + z * 3i) + z(2 + z))
-24i + 6iz + -16i2 + -3z + z2 = ((6i + 3iz) + z(2 + z))
-24i + 6iz + -16i2 + -3z + z2 = (6i + 3iz + (2 * z + z * z))
-24i + 6iz + -16i2 + -3z + z2 = (6i + 3iz + (2z + z2))
-24i + 6iz + -16i2 + -3z + z2 = (6i + 3iz + 2z + z2)

Add '-1z2' to each side of the equation.
-24i + 6iz + -16i2 + -3z + z2 + -1z2 = 6i + 3iz + 2z + z2 + -1z2

Combine like terms: z2 + -1z2 = 0
-24i + 6iz + -16i2 + -3z + 0 = 6i + 3iz + 2z + z2 + -1z2
-24i + 6iz + -16i2 + -3z = 6i + 3iz + 2z + z2 + -1z2

Combine like terms: z2 + -1z2 = 0
-24i + 6iz + -16i2 + -3z = 6i + 3iz + 2z + 0
-24i + 6iz + -16i2 + -3z = 6i + 3iz + 2z

Solving
-24i + 6iz + -16i2 + -3z = 6i + 3iz + 2z

Solving for variable 'i'.

Reorder the terms:
-24i + -6i + 6iz + -3iz + -16i2 + -3z + -2z = 6i + 3iz + 2z + -6i + -3iz + -2z

Combine like terms: -24i + -6i = -30i
-30i + 6iz + -3iz + -16i2 + -3z + -2z = 6i + 3iz + 2z + -6i + -3iz + -2z

Combine like terms: 6iz + -3iz = 3iz
-30i + 3iz + -16i2 + -3z + -2z = 6i + 3iz + 2z + -6i + -3iz + -2z

Combine like terms: -3z + -2z = -5z
-30i + 3iz + -16i2 + -5z = 6i + 3iz + 2z + -6i + -3iz + -2z

Reorder the terms:
-30i + 3iz + -16i2 + -5z = 6i + -6i + 3iz + -3iz + 2z + -2z

Combine like terms: 6i + -6i = 0
-30i + 3iz + -16i2 + -5z = 0 + 3iz + -3iz + 2z + -2z
-30i + 3iz + -16i2 + -5z = 3iz + -3iz + 2z + -2z

Combine like terms: 3iz + -3iz = 0
-30i + 3iz + -16i2 + -5z = 0 + 2z + -2z
-30i + 3iz + -16i2 + -5z = 2z + -2z

Combine like terms: 2z + -2z = 0
-30i + 3iz + -16i2 + -5z = 0

The solution to this equation could not be determined.

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