-k^2-2k-1=0

Solution for -k^2-2k-1=0 equation:

Simplifying
-1k2 + -2k + -1 = 0

Reorder the terms:
-1 + -2k + -1k2 = 0

Solving
-1 + -2k + -1k2 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(1 + 2k + k2) = 0

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

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

Simplifying
1 + k = 0

Solving
1 + k = 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 + k = 0 + -1

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

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

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

Simplifying
1 + k = 0

Solving
1 + k = 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 + k = 0 + -1

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

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

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