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

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

Simplifying
-9q2 + 6q + -1 = 0

Reorder the terms:
-1 + 6q + -9q2 = 0

Solving
-1 + 6q + -9q2 = 0

Solving for variable 'q'.

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

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

Simplifying
-1 + 3q = 0

Solving
-1 + 3q = 0

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

Add '1' to each side of the equation.
-1 + 1 + 3q = 0 + 1

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

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

Divide each side by '3'.
q = 0.3333333333

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

Simplifying
1 + -3q = 0

Solving
1 + -3q = 0

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

Add '-1' to each side of the equation.
1 + -1 + -3q = 0 + -1

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

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

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

Simplifying
q = 0.3333333333
Solution
q = {0.3333333333, 0.3333333333}