Z^4-2z^3+2z^2-2z+1=0

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Solution for Z^4-2z^3+2z^2-2z+1=0 equation:


Simplifying
Z4 + -2z3 + 2z2 + -2z + 1 = 0

Reorder the terms:
1 + Z4 + -2z + 2z2 + -2z3 = 0

Solving
1 + Z4 + -2z + 2z2 + -2z3 = 0

Solving for variable 'Z'.

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

Add '-1' to each side of the equation.
1 + Z4 + -2z + 2z2 + -1 + -2z3 = 0 + -1

Reorder the terms:
1 + -1 + Z4 + -2z + 2z2 + -2z3 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + Z4 + -2z + 2z2 + -2z3 = 0 + -1
Z4 + -2z + 2z2 + -2z3 = 0 + -1

Combine like terms: 0 + -1 = -1
Z4 + -2z + 2z2 + -2z3 = -1

Add '2z' to each side of the equation.
Z4 + -2z + 2z2 + 2z + -2z3 = -1 + 2z

Reorder the terms:
Z4 + -2z + 2z + 2z2 + -2z3 = -1 + 2z

Combine like terms: -2z + 2z = 0
Z4 + 0 + 2z2 + -2z3 = -1 + 2z
Z4 + 2z2 + -2z3 = -1 + 2z

Add '-2z2' to each side of the equation.
Z4 + 2z2 + -2z2 + -2z3 = -1 + 2z + -2z2

Combine like terms: 2z2 + -2z2 = 0
Z4 + 0 + -2z3 = -1 + 2z + -2z2
Z4 + -2z3 = -1 + 2z + -2z2

Add '2z3' to each side of the equation.
Z4 + -2z3 + 2z3 = -1 + 2z + -2z2 + 2z3

Combine like terms: -2z3 + 2z3 = 0
Z4 + 0 = -1 + 2z + -2z2 + 2z3
Z4 = -1 + 2z + -2z2 + 2z3

Simplifying
Z4 = -1 + 2z + -2z2 + 2z3

Reorder the terms:
1 + Z4 + -2z + 2z2 + -2z3 = -1 + 2z + -2z2 + 2z3 + 1 + -2z + 2z2 + -2z3

Reorder the terms:
1 + Z4 + -2z + 2z2 + -2z3 = -1 + 1 + 2z + -2z + -2z2 + 2z2 + 2z3 + -2z3

Combine like terms: -1 + 1 = 0
1 + Z4 + -2z + 2z2 + -2z3 = 0 + 2z + -2z + -2z2 + 2z2 + 2z3 + -2z3
1 + Z4 + -2z + 2z2 + -2z3 = 2z + -2z + -2z2 + 2z2 + 2z3 + -2z3

Combine like terms: 2z + -2z = 0
1 + Z4 + -2z + 2z2 + -2z3 = 0 + -2z2 + 2z2 + 2z3 + -2z3
1 + Z4 + -2z + 2z2 + -2z3 = -2z2 + 2z2 + 2z3 + -2z3

Combine like terms: -2z2 + 2z2 = 0
1 + Z4 + -2z + 2z2 + -2z3 = 0 + 2z3 + -2z3
1 + Z4 + -2z + 2z2 + -2z3 = 2z3 + -2z3

Combine like terms: 2z3 + -2z3 = 0
1 + Z4 + -2z + 2z2 + -2z3 = 0

The solution to this equation could not be determined.

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