n^2=2n-1

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

Simplifying
n2 = 2n + -1

Reorder the terms:
n2 = -1 + 2n

Solving
n2 = -1 + 2n

Solving for variable 'n'.

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

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

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

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

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

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

Simplifying
1 + -1n = 0

Solving
1 + -1n = 0

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

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

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

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

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

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

Simplifying
1 + -1n = 0

Solving
1 + -1n = 0

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

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

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

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

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

Simplifying
n = 1
Solution
n = {1, 1}