K^2-4K+1=6

Solution for K^2-4K+1=6 equation:

Simplifying
K2 + -4K + 1 = 6

Reorder the terms:
1 + -4K + K2 = 6

Solving
1 + -4K + K2 = 6

Solving for variable 'K'.

Reorder the terms:
1 + -6 + -4K + K2 = 6 + -6

Combine like terms: 1 + -6 = -5
-5 + -4K + K2 = 6 + -6

Combine like terms: 6 + -6 = 0
-5 + -4K + K2 = 0

Factor a trinomial.
(-1 + -1K)(5 + -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 '(5 + -1K)' equal to zero and attempt to solve:

Simplifying
5 + -1K = 0

Solving
5 + -1K = 0

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

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

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

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

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

Simplifying
K = 5
Solution
K = {-1, 5}