-24k^2-8k+16=0

Solution for -24k^2-8k+16=0 equation:

Simplifying
-24k2 + -8k + 16 = 0

Reorder the terms:
16 + -8k + -24k2 = 0

Solving
16 + -8k + -24k2 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), '8'.
8(2 + -1k + -3k2) = 0

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

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

Simplifying
2 + -3k = 0

Solving
2 + -3k = 0

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

Add '-2' to each side of the equation.
2 + -2 + -3k = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3k = 0 + -2
-3k = 0 + -2

Combine like terms: 0 + -2 = -2
-3k = -2

Divide each side by '-3'.
k = 0.6666666667

Simplifying
k = 0.6666666667
Subproblem 2
Set the factor '(1 + k)' equal to zero and attempt to solve:

Simplifying
1 + k = 0

Solving
1 + k = 0

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

Add '-1' to each side of the equation.
1 + -1 + k = 0 + -1

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

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

Simplifying
k = -1
Solution
k = {0.6666666667, -1}