z^1-z=-22(0)+a^2-2a+1

Solution for z^1-z=-22(0)+a^2-2a+1 equation:

Simplifying
z + -1z = -22(0) + a2 + -2a + 1

Combine like terms: z + -1z = 0
0 = -22(0) + a2 + -2a + 1

Multiply -22 * 0
0 = 0 + a2 + -2a + 1

Anything times zero is zero.
0 = 0 + a2 + -2a + 1

Reorder the terms:
0 = 0 + 1 + -2a + a2

Combine like terms: 0 + 1 = 1
0 = 1 + -2a + a2

Solving
0 = 1 + -2a + a2

Solving for variable 'a'.

Combine like terms: 0 + -1 = -1
-1 + 2a + -1a2 = 1 + -2a + a2 + -1 + 2a + -1a2

Reorder the terms:
-1 + 2a + -1a2 = 1 + -1 + -2a + 2a + a2 + -1a2

Combine like terms: 1 + -1 = 0
-1 + 2a + -1a2 = 0 + -2a + 2a + a2 + -1a2
-1 + 2a + -1a2 = -2a + 2a + a2 + -1a2

Combine like terms: -2a + 2a = 0
-1 + 2a + -1a2 = 0 + a2 + -1a2
-1 + 2a + -1a2 = a2 + -1a2

Combine like terms: a2 + -1a2 = 0
-1 + 2a + -1a2 = 0

Factor a trinomial.
(-1 + a)(1 + -1a) = 0

Subproblem 1
Set the factor '(-1 + a)' equal to zero and attempt to solve:

Simplifying
-1 + a = 0

Solving
-1 + a = 0

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

Add '1' to each side of the equation.
-1 + 1 + a = 0 + 1

Combine like terms: -1 + 1 = 0
0 + a = 0 + 1
a = 0 + 1

Combine like terms: 0 + 1 = 1
a = 1

Simplifying
a = 1
Subproblem 2
Set the factor '(1 + -1a)' equal to zero and attempt to solve:

Simplifying
1 + -1a = 0

Solving
1 + -1a = 0

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

Add '-1' to each side of the equation.
1 + -1 + -1a = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1a = 0 + -1
-1a = 0 + -1

Combine like terms: 0 + -1 = -1
-1a = -1

Divide each side by '-1'.
a = 1

Simplifying
a = 1
Solution
a = {1, 1}