-9k^2+6k-1=0

Solution for -9k^2+6k-1=0 equation:

Simplifying
-9k2 + 6k + -1 = 0

Reorder the terms:
-1 + 6k + -9k2 = 0

Solving
-1 + 6k + -9k2 = 0

Solving for variable 'k'.

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

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

Simplifying
-1 + 3k = 0

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

Combine like terms: -1 + 1 = 0
0 + 3k = 0 + 1
3k = 0 + 1

Combine like terms: 0 + 1 = 1
3k = 1

Divide each side by '3'.
k = 0.3333333333

Simplifying
k = 0.3333333333
Subproblem 2
Set the factor '(1 + -3k)' equal to zero and attempt to solve:

Simplifying
1 + -3k = 0

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

Combine like terms: 1 + -1 = 0
0 + -3k = 0 + -1
-3k = 0 + -1

Combine like terms: 0 + -1 = -1
-3k = -1

Divide each side by '-3'.
k = 0.3333333333

Simplifying
k = 0.3333333333
Solution
k = {0.3333333333, 0.3333333333}