n+1=n^2-2n+1

Solution for n+1=n^2-2n+1 equation:

Simplifying
n + 1 = n2 + -2n + 1

Reorder the terms:
1 + n = n2 + -2n + 1

Reorder the terms:
1 + n = 1 + -2n + n2

Add '-1' to each side of the equation.
1 + -1 + n = 1 + -2n + -1 + n2

Combine like terms: 1 + -1 = 0
0 + n = 1 + -2n + -1 + n2
n = 1 + -2n + -1 + n2

Reorder the terms:
n = 1 + -1 + -2n + n2

Combine like terms: 1 + -1 = 0
n = 0 + -2n + n2
n = -2n + n2

Solving
n = -2n + n2

Solving for variable 'n'.

Combine like terms: n + 2n = 3n
3n + -1n2 = -2n + n2 + 2n + -1n2

Reorder the terms:
3n + -1n2 = -2n + 2n + n2 + -1n2

Combine like terms: -2n + 2n = 0
3n + -1n2 = 0 + n2 + -1n2
3n + -1n2 = n2 + -1n2

Combine like terms: n2 + -1n2 = 0
3n + -1n2 = 0

Factor out the Greatest Common Factor (GCF), 'n'.
n(3 + -1n) = 0

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

Simplifying
n = 0

Solving
n = 0

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

Simplifying
n = 0
Subproblem 2
Set the factor '(3 + -1n)' equal to zero and attempt to solve:

Simplifying
3 + -1n = 0

Solving
3 + -1n = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1n = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1n = 0 + -3
-1n = 0 + -3

Combine like terms: 0 + -3 = -3
-1n = -3

Divide each side by '-1'.
n = 3

Simplifying
n = 3
Solution
n = {0, 3}