z^4-3(1+2i)z^2-8+6i=0

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Solution for z^4-3(1+2i)z^2-8+6i=0 equation: 


Simplifying
z4 + -3(1 + 2i) * z2 + -8 + 6i = 0

Reorder the terms for easier multiplication:
z4 + -3z2(1 + 2i) + -8 + 6i = 0
z4 + (1 * -3z2 + 2i * -3z2) + -8 + 6i = 0

Reorder the terms:
z4 + (-6iz2 + -3z2) + -8 + 6i = 0
z4 + (-6iz2 + -3z2) + -8 + 6i = 0

Reorder the terms:
-8 + 6i + -6iz2 + -3z2 + z4 = 0

Solving
-8 + 6i + -6iz2 + -3z2 + z4 = 0

Solving for variable 'i'.

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

Add '8' to each side of the equation.
-8 + 6i + -6iz2 + -3z2 + 8 + z4 = 0 + 8

Reorder the terms:
-8 + 8 + 6i + -6iz2 + -3z2 + z4 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + 6i + -6iz2 + -3z2 + z4 = 0 + 8
6i + -6iz2 + -3z2 + z4 = 0 + 8

Combine like terms: 0 + 8 = 8
6i + -6iz2 + -3z2 + z4 = 8

Add '3z2' to each side of the equation.
6i + -6iz2 + -3z2 + 3z2 + z4 = 8 + 3z2

Combine like terms: -3z2 + 3z2 = 0
6i + -6iz2 + 0 + z4 = 8 + 3z2
6i + -6iz2 + z4 = 8 + 3z2

Add '-1z4' to each side of the equation.
6i + -6iz2 + z4 + -1z4 = 8 + 3z2 + -1z4

Combine like terms: z4 + -1z4 = 0
6i + -6iz2 + 0 = 8 + 3z2 + -1z4
6i + -6iz2 = 8 + 3z2 + -1z4

Reorder the terms:
-8 + 6i + -6iz2 + -3z2 + z4 = 8 + 3z2 + -1z4 + -8 + -3z2 + z4

Reorder the terms:
-8 + 6i + -6iz2 + -3z2 + z4 = 8 + -8 + 3z2 + -3z2 + -1z4 + z4

Combine like terms: 8 + -8 = 0
-8 + 6i + -6iz2 + -3z2 + z4 = 0 + 3z2 + -3z2 + -1z4 + z4
-8 + 6i + -6iz2 + -3z2 + z4 = 3z2 + -3z2 + -1z4 + z4

Combine like terms: 3z2 + -3z2 = 0
-8 + 6i + -6iz2 + -3z2 + z4 = 0 + -1z4 + z4
-8 + 6i + -6iz2 + -3z2 + z4 = -1z4 + z4

Combine like terms: -1z4 + z4 = 0
-8 + 6i + -6iz2 + -3z2 + z4 = 0

The solution to this equation could not be determined.

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