z=(2+5i)(-4+2i+z)

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Solution for z=(2+5i)(-4+2i+z) equation: 


Simplifying
z = (2 + 5i)(-4 + 2i + z)

Multiply (2 + 5i) * (-4 + 2i + z)
z = (2(-4 + 2i + z) + 5i * (-4 + 2i + z))
z = ((-4 * 2 + 2i * 2 + z * 2) + 5i * (-4 + 2i + z))
z = ((-8 + 4i + 2z) + 5i * (-4 + 2i + z))
z = (-8 + 4i + 2z + (-4 * 5i + 2i * 5i + z * 5i))

Reorder the terms:
z = (-8 + 4i + 2z + (-20i + 5iz + 10i2))
z = (-8 + 4i + 2z + (-20i + 5iz + 10i2))

Reorder the terms:
z = (-8 + 4i + -20i + 5iz + 10i2 + 2z)

Combine like terms: 4i + -20i = -16i
z = (-8 + -16i + 5iz + 10i2 + 2z)

Solving
z = -8 + -16i + 5iz + 10i2 + 2z

Solving for variable 'z'.

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

Add '-5iz' to each side of the equation.
-5iz + z = -8 + -16i + 5iz + 10i2 + -5iz + 2z

Reorder the terms:
-5iz + z = -8 + -16i + 5iz + -5iz + 10i2 + 2z

Combine like terms: 5iz + -5iz = 0
-5iz + z = -8 + -16i + 0 + 10i2 + 2z
-5iz + z = -8 + -16i + 10i2 + 2z

Add '-2z' to each side of the equation.
-5iz + z + -2z = -8 + -16i + 10i2 + 2z + -2z

Combine like terms: z + -2z = -1z
-5iz + -1z = -8 + -16i + 10i2 + 2z + -2z

Combine like terms: 2z + -2z = 0
-5iz + -1z = -8 + -16i + 10i2 + 0
-5iz + -1z = -8 + -16i + 10i2

Reorder the terms:
8 + 16i + -5iz + -10i2 + -1z = -8 + -16i + 10i2 + 8 + 16i + -10i2

Reorder the terms:
8 + 16i + -5iz + -10i2 + -1z = -8 + 8 + -16i + 16i + 10i2 + -10i2

Combine like terms: -8 + 8 = 0
8 + 16i + -5iz + -10i2 + -1z = 0 + -16i + 16i + 10i2 + -10i2
8 + 16i + -5iz + -10i2 + -1z = -16i + 16i + 10i2 + -10i2

Combine like terms: -16i + 16i = 0
8 + 16i + -5iz + -10i2 + -1z = 0 + 10i2 + -10i2
8 + 16i + -5iz + -10i2 + -1z = 10i2 + -10i2

Combine like terms: 10i2 + -10i2 = 0
8 + 16i + -5iz + -10i2 + -1z = 0

The solution to this equation could not be determined.

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