10k^2-3k-1=0

Solution for 10k^2-3k-1=0 equation:

Simplifying
10k2 + -3k + -1 = 0

Reorder the terms:
-1 + -3k + 10k2 = 0

Solving
-1 + -3k + 10k2 = 0

Solving for variable 'k'.

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

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

Simplifying
-1 + -5k = 0

Solving
-1 + -5k = 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 + -5k = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -5k = 0 + 1
-5k = 0 + 1

Combine like terms: 0 + 1 = 1
-5k = 1

Divide each side by '-5'.
k = -0.2

Simplifying
k = -0.2
Subproblem 2
Set the factor '(1 + -2k)' equal to zero and attempt to solve:

Simplifying
1 + -2k = 0

Solving
1 + -2k = 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 + -2k = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2k = 0 + -1
-2k = 0 + -1

Combine like terms: 0 + -1 = -1
-2k = -1

Divide each side by '-2'.
k = 0.5

Simplifying
k = 0.5
Solution
k = {-0.2, 0.5}