24k^2+88k+64=0

Solution for 24k^2+88k+64=0 equation:

Simplifying
24k2 + 88k + 64 = 0

Reorder the terms:
64 + 88k + 24k2 = 0

Solving
64 + 88k + 24k2 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), '8'.
8(8 + 11k + 3k2) = 0

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

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

Simplifying
8 + 3k = 0

Solving
8 + 3k = 0

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

Add '-8' to each side of the equation.
8 + -8 + 3k = 0 + -8

Combine like terms: 8 + -8 = 0
0 + 3k = 0 + -8
3k = 0 + -8

Combine like terms: 0 + -8 = -8
3k = -8

Divide each side by '3'.
k = -2.666666667

Simplifying
k = -2.666666667
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 = {-2.666666667, -1}