16k^2-88k=-120

Solution for 16k^2-88k=-120 equation:

Simplifying
16k2 + -88k = -120

Reorder the terms:
-88k + 16k2 = -120

Solving
-88k + 16k2 = -120

Solving for variable 'k'.

Reorder the terms:
120 + -88k + 16k2 = -120 + 120

Combine like terms: -120 + 120 = 0
120 + -88k + 16k2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(15 + -11k + 2k2) = 0

Factor a trinomial.
8((5 + -2k)(3 + -1k)) = 0

Ignore the factor 8.
Subproblem 1
Set the factor '(5 + -2k)' equal to zero and attempt to solve:

Simplifying
5 + -2k = 0

Solving
5 + -2k = 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 + -2k = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2k = 0 + -5
-2k = 0 + -5

Combine like terms: 0 + -5 = -5
-2k = -5

Divide each side by '-2'.
k = 2.5

Simplifying
k = 2.5
Subproblem 2
Set the factor '(3 + -1k)' equal to zero and attempt to solve:

Simplifying
3 + -1k = 0

Solving
3 + -1k = 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 + -1k = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1k = 0 + -3
-1k = 0 + -3

Combine like terms: 0 + -3 = -3
-1k = -3

Divide each side by '-1'.
k = 3

Simplifying
k = 3
Solution
k = {2.5, 3}