(x^2-6x+6)=1

Solution for (x^2-6x+6)=1 equation:

Simplifying
(x2 + -6x + 6) = 1

Reorder the terms:
(6 + -6x + x2) = 1

Remove parenthesis around (6 + -6x + x2)
6 + -6x + x2 = 1

Solving
6 + -6x + x2 = 1

Solving for variable 'x'.

Reorder the terms:
6 + -1 + -6x + x2 = 1 + -1

Combine like terms: 6 + -1 = 5
5 + -6x + x2 = 1 + -1

Combine like terms: 1 + -1 = 0
5 + -6x + x2 = 0

Factor a trinomial.
(1 + -1x)(5 + -1x) = 0

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

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

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

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

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

Simplifying
x = 1
Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {1, 5}