z=3i(z-i)-5z

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


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

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

Reorder the terms:
z = (3iz + -3i2) + -5z
z = (3iz + -3i2) + -5z

Solving
z = 3iz + -3i2 + -5z

Solving for variable 'z'.

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

Add '-3iz' to each side of the equation.
-3iz + z = 3iz + -3i2 + -3iz + -5z

Reorder the terms:
-3iz + z = 3iz + -3iz + -3i2 + -5z

Combine like terms: 3iz + -3iz = 0
-3iz + z = 0 + -3i2 + -5z
-3iz + z = -3i2 + -5z

Add '5z' to each side of the equation.
-3iz + z + 5z = -3i2 + -5z + 5z

Combine like terms: z + 5z = 6z
-3iz + 6z = -3i2 + -5z + 5z

Combine like terms: -5z + 5z = 0
-3iz + 6z = -3i2 + 0
-3iz + 6z = -3i2

Reorder the terms:
-3iz + 3i2 + 6z = -3i2 + 3i2

Combine like terms: -3i2 + 3i2 = 0
-3iz + 3i2 + 6z = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-1iz + i2 + 2z) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-1iz + i2 + 2z)' equal to zero and attempt to solve:

Simplifying
-1iz + i2 + 2z = 0

Solving
-1iz + i2 + 2z = 0

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

Add '-1i2' to each side of the equation.
-1iz + i2 + -1i2 + 2z = 0 + -1i2

Combine like terms: i2 + -1i2 = 0
-1iz + 0 + 2z = 0 + -1i2
-1iz + 2z = 0 + -1i2
Remove the zero:
-1iz + 2z = -1i2

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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