10k^2+24k+8=0

Solution for 10k^2+24k+8=0 equation:

Simplifying
10k2 + 24k + 8 = 0

Reorder the terms:
8 + 24k + 10k2 = 0

Solving
8 + 24k + 10k2 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), '2'.
2(4 + 12k + 5k2) = 0

Factor a trinomial.
2((2 + k)(2 + 5k)) = 0

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

Simplifying
2 + k = 0

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

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

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

Simplifying
k = -2
Subproblem 2
Set the factor '(2 + 5k)' equal to zero and attempt to solve:

Simplifying
2 + 5k = 0

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

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

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

Divide each side by '5'.
k = -0.4

Simplifying
k = -0.4
Solution
k = {-2, -0.4}