k^2-4k+1=-2

Solution for k^2-4k+1=-2 equation:

Simplifying
k2 + -4k + 1 = -2

Reorder the terms:
1 + -4k + k2 = -2

Solving
1 + -4k + k2 = -2

Solving for variable 'k'.

Reorder the terms:
1 + 2 + -4k + k2 = -2 + 2

Combine like terms: 1 + 2 = 3
3 + -4k + k2 = -2 + 2

Combine like terms: -2 + 2 = 0
3 + -4k + k2 = 0

Factor a trinomial.
(1 + -1k)(3 + -1k) = 0

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

Simplifying
1 + -1k = 0

Solving
1 + -1k = 0

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

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

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

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

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

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

Simplifying
3 + -1k = 0

Solving
3 + -1k = 0

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

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

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

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

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

Simplifying
k = 3
Solution
k = {1, 3}