k^2-6k-1=-7-k

Solution for k^2-6k-1=-7-k equation:

Simplifying
k2 + -6k + -1 = -7 + -1k

Reorder the terms:
-1 + -6k + k2 = -7 + -1k

Solving
-1 + -6k + k2 = -7 + -1k

Solving for variable 'k'.

Reorder the terms:
-1 + 7 + -6k + k + k2 = -7 + -1k + 7 + k

Combine like terms: -1 + 7 = 6
6 + -6k + k + k2 = -7 + -1k + 7 + k

Combine like terms: -6k + k = -5k
6 + -5k + k2 = -7 + -1k + 7 + k

Reorder the terms:
6 + -5k + k2 = -7 + 7 + -1k + k

Combine like terms: -7 + 7 = 0
6 + -5k + k2 = 0 + -1k + k
6 + -5k + k2 = -1k + k

Combine like terms: -1k + k = 0
6 + -5k + k2 = 0

Factor a trinomial.
(2 + -1k)(3 + -1k) = 0

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

Simplifying
2 + -1k = 0

Solving
2 + -1k = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1k = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1k = 0 + -2
-1k = 0 + -2

Combine like terms: 0 + -2 = -2
-1k = -2

Divide each side by '-1'.
k = 2

Simplifying
k = 2
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 = {2, 3}