48k^2+162k+54=0

Solution for 48k^2+162k+54=0 equation:

Simplifying
48k2 + 162k + 54 = 0

Reorder the terms:
54 + 162k + 48k2 = 0

Solving
54 + 162k + 48k2 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), '6'.
6(9 + 27k + 8k2) = 0

Factor a trinomial.
6((3 + k)(3 + 8k)) = 0

Ignore the factor 6.
Subproblem 1
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
Subproblem 2
Set the factor '(3 + 8k)' equal to zero and attempt to solve:

Simplifying
3 + 8k = 0

Solving
3 + 8k = 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 + 8k = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 8k = 0 + -3
8k = 0 + -3

Combine like terms: 0 + -3 = -3
8k = -3

Divide each side by '8'.
k = -0.375

Simplifying
k = -0.375
Solution
k = {-3, -0.375}