6k^2+54k+48=0

Solution for 6k^2+54k+48=0 equation:

Simplifying
6k2 + 54k + 48 = 0

Reorder the terms:
48 + 54k + 6k2 = 0

Solving
48 + 54k + 6k2 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), '6'.
6(8 + 9k + k2) = 0

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

Ignore the factor 6.
Subproblem 1
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
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 = {-8, -1}