z^4+(-4+3i)z^2+(9+7i)z-(18+6i)=0

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Solution for z^4+(-4+3i)z^2+(9+7i)z-(18+6i)=0 equation: 


Simplifying
z4 + (-4 + 3i) * z2 + (9 + 7i) * z + -1(18 + 6i) = 0

Reorder the terms for easier multiplication:
z4 + z2(-4 + 3i) + (9 + 7i) * z + -1(18 + 6i) = 0
z4 + (-4 * z2 + 3i * z2) + (9 + 7i) * z + -1(18 + 6i) = 0

Reorder the terms:
z4 + (3iz2 + -4z2) + (9 + 7i) * z + -1(18 + 6i) = 0
z4 + (3iz2 + -4z2) + (9 + 7i) * z + -1(18 + 6i) = 0

Reorder the terms for easier multiplication:
z4 + 3iz2 + -4z2 + z(9 + 7i) + -1(18 + 6i) = 0
z4 + 3iz2 + -4z2 + (9 * z + 7i * z) + -1(18 + 6i) = 0

Reorder the terms:
z4 + 3iz2 + -4z2 + (7iz + 9z) + -1(18 + 6i) = 0
z4 + 3iz2 + -4z2 + (7iz + 9z) + -1(18 + 6i) = 0
z4 + 3iz2 + -4z2 + 7iz + 9z + (18 * -1 + 6i * -1) = 0
z4 + 3iz2 + -4z2 + 7iz + 9z + (-18 + -6i) = 0

Reorder the terms:
-18 + -6i + 7iz + 3iz2 + 9z + -4z2 + z4 = 0

Solving
-18 + -6i + 7iz + 3iz2 + 9z + -4z2 + z4 = 0

Solving for variable 'i'.

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

Add '18' to each side of the equation.
-18 + -6i + 7iz + 3iz2 + 9z + -4z2 + 18 + z4 = 0 + 18

Reorder the terms:
-18 + 18 + -6i + 7iz + 3iz2 + 9z + -4z2 + z4 = 0 + 18

Combine like terms: -18 + 18 = 0
0 + -6i + 7iz + 3iz2 + 9z + -4z2 + z4 = 0 + 18
-6i + 7iz + 3iz2 + 9z + -4z2 + z4 = 0 + 18

Combine like terms: 0 + 18 = 18
-6i + 7iz + 3iz2 + 9z + -4z2 + z4 = 18

Add '-9z' to each side of the equation.
-6i + 7iz + 3iz2 + 9z + -4z2 + -9z + z4 = 18 + -9z

Reorder the terms:
-6i + 7iz + 3iz2 + 9z + -9z + -4z2 + z4 = 18 + -9z

Combine like terms: 9z + -9z = 0
-6i + 7iz + 3iz2 + 0 + -4z2 + z4 = 18 + -9z
-6i + 7iz + 3iz2 + -4z2 + z4 = 18 + -9z

Add '4z2' to each side of the equation.
-6i + 7iz + 3iz2 + -4z2 + 4z2 + z4 = 18 + -9z + 4z2

Combine like terms: -4z2 + 4z2 = 0
-6i + 7iz + 3iz2 + 0 + z4 = 18 + -9z + 4z2
-6i + 7iz + 3iz2 + z4 = 18 + -9z + 4z2

Add '-1z4' to each side of the equation.
-6i + 7iz + 3iz2 + z4 + -1z4 = 18 + -9z + 4z2 + -1z4

Combine like terms: z4 + -1z4 = 0
-6i + 7iz + 3iz2 + 0 = 18 + -9z + 4z2 + -1z4
-6i + 7iz + 3iz2 = 18 + -9z + 4z2 + -1z4

Reorder the terms:
-18 + -6i + 7iz + 3iz2 + 9z + -4z2 + z4 = 18 + -9z + 4z2 + -1z4 + -18 + 9z + -4z2 + z4

Reorder the terms:
-18 + -6i + 7iz + 3iz2 + 9z + -4z2 + z4 = 18 + -18 + -9z + 9z + 4z2 + -4z2 + -1z4 + z4

Combine like terms: 18 + -18 = 0
-18 + -6i + 7iz + 3iz2 + 9z + -4z2 + z4 = 0 + -9z + 9z + 4z2 + -4z2 + -1z4 + z4
-18 + -6i + 7iz + 3iz2 + 9z + -4z2 + z4 = -9z + 9z + 4z2 + -4z2 + -1z4 + z4

Combine like terms: -9z + 9z = 0
-18 + -6i + 7iz + 3iz2 + 9z + -4z2 + z4 = 0 + 4z2 + -4z2 + -1z4 + z4
-18 + -6i + 7iz + 3iz2 + 9z + -4z2 + z4 = 4z2 + -4z2 + -1z4 + z4

Combine like terms: 4z2 + -4z2 = 0
-18 + -6i + 7iz + 3iz2 + 9z + -4z2 + z4 = 0 + -1z4 + z4
-18 + -6i + 7iz + 3iz2 + 9z + -4z2 + z4 = -1z4 + z4

Combine like terms: -1z4 + z4 = 0
-18 + -6i + 7iz + 3iz2 + 9z + -4z2 + z4 = 0

The solution to this equation could not be determined.

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