48-2k-k^2=0

Solution for 48-2k-k^2=0 equation:

Simplifying
48 + -2k + -1k2 = 0

Solving
48 + -2k + -1k2 = 0

Solving for variable 'k'.

Factor a trinomial.
(6 + -1k)(8 + k) = 0

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

Simplifying
6 + -1k = 0

Solving
6 + -1k = 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 + -1k = 0 + -6

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

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

Divide each side by '-1'.
k = 6

Simplifying
k = 6
Subproblem 2
Set the factor '(8 + k)' equal to zero and attempt to solve:

Simplifying
8 + k = 0

Solving
8 + k = 0

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

Add '-8' to each side of the equation.
8 + -8 + k = 0 + -8

Combine like terms: 8 + -8 = 0
0 + k = 0 + -8
k = 0 + -8

Combine like terms: 0 + -8 = -8
k = -8

Simplifying
k = -8
Solution
k = {6, -8}