0=-7k-12-k^2

Solution for 0=-7k-12-k^2 equation:

Simplifying
0 = -7k + -12 + -1k2

Reorder the terms:
0 = -12 + -7k + -1k2

Solving
0 = -12 + -7k + -1k2

Solving for variable 'k'.

Combine like terms: 0 + 12 = 12
12 + 7k + k2 = -12 + -7k + -1k2 + 12 + 7k + k2

Reorder the terms:
12 + 7k + k2 = -12 + 12 + -7k + 7k + -1k2 + k2

Combine like terms: -12 + 12 = 0
12 + 7k + k2 = 0 + -7k + 7k + -1k2 + k2
12 + 7k + k2 = -7k + 7k + -1k2 + k2

Combine like terms: -7k + 7k = 0
12 + 7k + k2 = 0 + -1k2 + k2
12 + 7k + k2 = -1k2 + k2

Combine like terms: -1k2 + k2 = 0
12 + 7k + k2 = 0

Factor a trinomial.
(4 + k)(3 + k) = 0

Subproblem 1
Set the factor '(4 + k)' equal to zero and attempt to solve:

Simplifying
4 + k = 0

Solving
4 + k = 0

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

Add '-4' to each side of the equation.
4 + -4 + k = 0 + -4

Combine like terms: 4 + -4 = 0
0 + k = 0 + -4
k = 0 + -4

Combine like terms: 0 + -4 = -4
k = -4

Simplifying
k = -4
Subproblem 2
Set the factor '(3 + k)' equal to zero and attempt to solve:

Simplifying
3 + k = 0

Solving
3 + k = 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 + k = 0 + -3

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

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

Simplifying
k = -3
Solution
k = {-4, -3}