8k^2+53k+30=0

Solution for 8k^2+53k+30=0 equation:

Simplifying
8k2 + 53k + 30 = 0

Reorder the terms:
30 + 53k + 8k2 = 0

Solving
30 + 53k + 8k2 = 0

Solving for variable 'k'.

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

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 + 8k)' equal to zero and attempt to solve:

Simplifying
5 + 8k = 0

Solving
5 + 8k = 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 + 8k = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 8k = 0 + -5
8k = 0 + -5

Combine like terms: 0 + -5 = -5
8k = -5

Divide each side by '8'.
k = -0.625

Simplifying
k = -0.625
Solution
k = {-6, -0.625}