(2+i)z^2-(5-i)z+(2-2i)=0

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Solution for (2+i)z^2-(5-i)z+(2-2i)=0 equation: 


Simplifying
(2 + i) * z2 + -1(5 + -1i) * z + (2 + -2i) = 0

Reorder the terms for easier multiplication:
z2(2 + i) + -1(5 + -1i) * z + (2 + -2i) = 0
(2 * z2 + i * z2) + -1(5 + -1i) * z + (2 + -2i) = 0

Reorder the terms:
(iz2 + 2z2) + -1(5 + -1i) * z + (2 + -2i) = 0
(iz2 + 2z2) + -1(5 + -1i) * z + (2 + -2i) = 0

Reorder the terms for easier multiplication:
iz2 + 2z2 + -1z(5 + -1i) + (2 + -2i) = 0
iz2 + 2z2 + (5 * -1z + -1i * -1z) + (2 + -2i) = 0

Reorder the terms:
iz2 + 2z2 + (1iz + -5z) + (2 + -2i) = 0
iz2 + 2z2 + (1iz + -5z) + (2 + -2i) = 0

Remove parenthesis around (2 + -2i)
iz2 + 2z2 + 1iz + -5z + 2 + -2i = 0

Reorder the terms:
2 + -2i + 1iz + iz2 + -5z + 2z2 = 0

Solving
2 + -2i + 1iz + iz2 + -5z + 2z2 = 0

Solving for variable 'i'.

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

Add '-2' to each side of the equation.
2 + -2i + 1iz + iz2 + -5z + -2 + 2z2 = 0 + -2

Reorder the terms:
2 + -2 + -2i + 1iz + iz2 + -5z + 2z2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -2i + 1iz + iz2 + -5z + 2z2 = 0 + -2
-2i + 1iz + iz2 + -5z + 2z2 = 0 + -2

Combine like terms: 0 + -2 = -2
-2i + 1iz + iz2 + -5z + 2z2 = -2

Add '5z' to each side of the equation.
-2i + 1iz + iz2 + -5z + 5z + 2z2 = -2 + 5z

Combine like terms: -5z + 5z = 0
-2i + 1iz + iz2 + 0 + 2z2 = -2 + 5z
-2i + 1iz + iz2 + 2z2 = -2 + 5z

Add '-2z2' to each side of the equation.
-2i + 1iz + iz2 + 2z2 + -2z2 = -2 + 5z + -2z2

Combine like terms: 2z2 + -2z2 = 0
-2i + 1iz + iz2 + 0 = -2 + 5z + -2z2
-2i + 1iz + iz2 = -2 + 5z + -2z2

Reorder the terms:
2 + -2i + 1iz + iz2 + -5z + 2z2 = -2 + 5z + -2z2 + 2 + -5z + 2z2

Reorder the terms:
2 + -2i + 1iz + iz2 + -5z + 2z2 = -2 + 2 + 5z + -5z + -2z2 + 2z2

Combine like terms: -2 + 2 = 0
2 + -2i + 1iz + iz2 + -5z + 2z2 = 0 + 5z + -5z + -2z2 + 2z2
2 + -2i + 1iz + iz2 + -5z + 2z2 = 5z + -5z + -2z2 + 2z2

Combine like terms: 5z + -5z = 0
2 + -2i + 1iz + iz2 + -5z + 2z2 = 0 + -2z2 + 2z2
2 + -2i + 1iz + iz2 + -5z + 2z2 = -2z2 + 2z2

Combine like terms: -2z2 + 2z2 = 0
2 + -2i + 1iz + iz2 + -5z + 2z2 = 0

The solution to this equation could not be determined.

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