(n-1)*(n-2)=1

Solution for (n-1)*(n-2)=1 equation:

Simplifying
(n + -1)(n + -2) = 1

Reorder the terms:
(-1 + n)(n + -2) = 1

Reorder the terms:
(-1 + n)(-2 + n) = 1

Multiply (-1 + n) * (-2 + n)
(-1(-2 + n) + n(-2 + n)) = 1
((-2 * -1 + n * -1) + n(-2 + n)) = 1
((2 + -1n) + n(-2 + n)) = 1
(2 + -1n + (-2 * n + n * n)) = 1
(2 + -1n + (-2n + n2)) = 1

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

Solving
2 + -3n + n2 = 1

Solving for variable 'n'.

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

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

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

Begin completing the square.

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + -3n + -1 + n2 = 0 + -1

Reorder the terms:
1 + -1 + -3n + n2 = 0 + -1

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

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

The n term is -3n.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3n + 2.25 + n2 = -1 + 2.25

Reorder the terms:
2.25 + -3n + n2 = -1 + 2.25

Combine like terms: -1 + 2.25 = 1.25
2.25 + -3n + n2 = 1.25

Factor a perfect square on the left side:
(n + -1.5)(n + -1.5) = 1.25

Calculate the square root of the right side: 1.118033989

Break this problem into two subproblems by setting 
(n + -1.5) equal to 1.118033989 and -1.118033989.

Subproblem 1
n + -1.5 = 1.118033989

Simplifying
n + -1.5 = 1.118033989

Reorder the terms:
-1.5 + n = 1.118033989

Solving
-1.5 + n = 1.118033989

Solving for variable 'n'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + n = 1.118033989 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + n = 1.118033989 + 1.5
n = 1.118033989 + 1.5

Combine like terms: 1.118033989 + 1.5 = 2.618033989
n = 2.618033989

Simplifying
n = 2.618033989

Subproblem 2
n + -1.5 = -1.118033989

Simplifying
n + -1.5 = -1.118033989

Reorder the terms:
-1.5 + n = -1.118033989

Solving
-1.5 + n = -1.118033989

Solving for variable 'n'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + n = -1.118033989 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + n = -1.118033989 + 1.5
n = -1.118033989 + 1.5

Combine like terms: -1.118033989 + 1.5 = 0.381966011
n = 0.381966011

Simplifying
n = 0.381966011

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {2.618033989, 0.381966011}