8k^2+80k=-192

Solution for 8k^2+80k=-192 equation:

Simplifying
8k2 + 80k = -192

Reorder the terms:
80k + 8k2 = -192

Solving
80k + 8k2 = -192

Solving for variable 'k'.

Reorder the terms:
192 + 80k + 8k2 = -192 + 192

Combine like terms: -192 + 192 = 0
192 + 80k + 8k2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(24 + 10k + k2) = 0

Factor a trinomial.
8((6 + k)(4 + k)) = 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 '(4 + k)' equal to zero and attempt to solve:

Simplifying
4 + k = 0

Solving
4 + k = 0

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

Add '-4' to each side of the equation.
4 + -4 + k = 0 + -4

Combine like terms: 4 + -4 = 0
0 + k = 0 + -4
k = 0 + -4

Combine like terms: 0 + -4 = -4
k = -4

Simplifying
k = -4
Solution
k = {-6, -4}