(a^2-2a+1)=1

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

Simplifying
(a2 + -2a + 1) = 1

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

Remove parenthesis around (1 + -2a + a2)
1 + -2a + a2 = 1

Add '-1' to each side of the equation.
1 + -2a + -1 + a2 = 1 + -1

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

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

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

Solving
-2a + a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), 'a'.
a(-2 + a) = 0

Subproblem 1
Set the factor 'a' equal to zero and attempt to solve:

Simplifying
a = 0

Solving
a = 0

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

Simplifying
a = 0
Subproblem 2
Set the factor '(-2 + a)' equal to zero and attempt to solve:

Simplifying
-2 + a = 0

Solving
-2 + a = 0

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

Add '2' to each side of the equation.
-2 + 2 + a = 0 + 2

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

Combine like terms: 0 + 2 = 2
a = 2

Simplifying
a = 2
Solution
a = {0, 2}