24k^2+184k=-240

Solution for 24k^2+184k=-240 equation:

Simplifying
24k2 + 184k = -240

Reorder the terms:
184k + 24k2 = -240

Solving
184k + 24k2 = -240

Solving for variable 'k'.

Reorder the terms:
240 + 184k + 24k2 = -240 + 240

Combine like terms: -240 + 240 = 0
240 + 184k + 24k2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(30 + 23k + 3k2) = 0

Factor a trinomial.
8((6 + k)(5 + 3k)) = 0

Ignore the factor 8.
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 '(5 + 3k)' equal to zero and attempt to solve:

Simplifying
5 + 3k = 0

Solving
5 + 3k = 0

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

Add '-5' to each side of the equation.
5 + -5 + 3k = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 3k = 0 + -5
3k = 0 + -5

Combine like terms: 0 + -5 = -5
3k = -5

Divide each side by '3'.
k = -1.666666667

Simplifying
k = -1.666666667
Solution
k = {-6, -1.666666667}