(2+i)*z^2-(3-2i)*z-(1+2i)=0

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


Simplifying
(2 + i) * z2 + -1(3 + -2i) * z + -1(1 + 2i) = 0

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

Reorder the terms:
(iz2 + 2z2) + -1(3 + -2i) * z + -1(1 + 2i) = 0
(iz2 + 2z2) + -1(3 + -2i) * z + -1(1 + 2i) = 0

Reorder the terms for easier multiplication:
iz2 + 2z2 + -1z(3 + -2i) + -1(1 + 2i) = 0
iz2 + 2z2 + (3 * -1z + -2i * -1z) + -1(1 + 2i) = 0

Reorder the terms:
iz2 + 2z2 + (2iz + -3z) + -1(1 + 2i) = 0
iz2 + 2z2 + (2iz + -3z) + -1(1 + 2i) = 0
iz2 + 2z2 + 2iz + -3z + (1 * -1 + 2i * -1) = 0
iz2 + 2z2 + 2iz + -3z + (-1 + -2i) = 0

Reorder the terms:
-1 + -2i + 2iz + iz2 + -3z + 2z2 = 0

Solving
-1 + -2i + 2iz + iz2 + -3z + 2z2 = 0

Solving for variable 'i'.

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

Add '1' to each side of the equation.
-1 + -2i + 2iz + iz2 + -3z + 1 + 2z2 = 0 + 1

Reorder the terms:
-1 + 1 + -2i + 2iz + iz2 + -3z + 2z2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -2i + 2iz + iz2 + -3z + 2z2 = 0 + 1
-2i + 2iz + iz2 + -3z + 2z2 = 0 + 1

Combine like terms: 0 + 1 = 1
-2i + 2iz + iz2 + -3z + 2z2 = 1

Add '3z' to each side of the equation.
-2i + 2iz + iz2 + -3z + 3z + 2z2 = 1 + 3z

Combine like terms: -3z + 3z = 0
-2i + 2iz + iz2 + 0 + 2z2 = 1 + 3z
-2i + 2iz + iz2 + 2z2 = 1 + 3z

Add '-2z2' to each side of the equation.
-2i + 2iz + iz2 + 2z2 + -2z2 = 1 + 3z + -2z2

Combine like terms: 2z2 + -2z2 = 0
-2i + 2iz + iz2 + 0 = 1 + 3z + -2z2
-2i + 2iz + iz2 = 1 + 3z + -2z2

Reorder the terms:
-1 + -2i + 2iz + iz2 + -3z + 2z2 = 1 + 3z + -2z2 + -1 + -3z + 2z2

Reorder the terms:
-1 + -2i + 2iz + iz2 + -3z + 2z2 = 1 + -1 + 3z + -3z + -2z2 + 2z2

Combine like terms: 1 + -1 = 0
-1 + -2i + 2iz + iz2 + -3z + 2z2 = 0 + 3z + -3z + -2z2 + 2z2
-1 + -2i + 2iz + iz2 + -3z + 2z2 = 3z + -3z + -2z2 + 2z2

Combine like terms: 3z + -3z = 0
-1 + -2i + 2iz + iz2 + -3z + 2z2 = 0 + -2z2 + 2z2
-1 + -2i + 2iz + iz2 + -3z + 2z2 = -2z2 + 2z2

Combine like terms: -2z2 + 2z2 = 0
-1 + -2i + 2iz + iz2 + -3z + 2z2 = 0

The solution to this equation could not be determined.

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