-5k^2-8k-3=0

Solution for -5k^2-8k-3=0 equation:

Simplifying
-5k2 + -8k + -3 = 0

Reorder the terms:
-3 + -8k + -5k2 = 0

Solving
-3 + -8k + -5k2 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(3 + 8k + 5k2) = 0

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

Ignore the factor -1.
Subproblem 1
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
Subproblem 2
Set the factor '(3 + 5k)' equal to zero and attempt to solve:

Simplifying
3 + 5k = 0

Solving
3 + 5k = 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 + 5k = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 5k = 0 + -3
5k = 0 + -3

Combine like terms: 0 + -3 = -3
5k = -3

Divide each side by '5'.
k = -0.6

Simplifying
k = -0.6
Solution
k = {-1, -0.6}