6=-k^2-7k

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

Simplifying
6 = -1k2 + -7k

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

Solving
6 = -7k + -1k2

Solving for variable 'k'.

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

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

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

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

Subproblem 1
Set the factor '(6 + k)' equal to zero and attempt to solve:

Simplifying
6 + k = 0

Solving
6 + k = 0

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

Add '-6' to each side of the equation.
6 + -6 + k = 0 + -6

Combine like terms: 6 + -6 = 0
0 + k = 0 + -6
k = 0 + -6

Combine like terms: 0 + -6 = -6
k = -6

Simplifying
k = -6
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 = {-6, -1}