30w^2-11w+1=0

Solution for 30w^2-11w+1=0 equation:

Simplifying
30w2 + -11w + 1 = 0

Reorder the terms:
1 + -11w + 30w2 = 0

Solving
1 + -11w + 30w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(1 + -6w)(1 + -5w) = 0

Subproblem 1
Set the factor '(1 + -6w)' equal to zero and attempt to solve:

Simplifying
1 + -6w = 0

Solving
1 + -6w = 0

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

Add '-1' to each side of the equation.
1 + -1 + -6w = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -6w = 0 + -1
-6w = 0 + -1

Combine like terms: 0 + -1 = -1
-6w = -1

Divide each side by '-6'.
w = 0.1666666667

Simplifying
w = 0.1666666667
Subproblem 2
Set the factor '(1 + -5w)' equal to zero and attempt to solve:

Simplifying
1 + -5w = 0

Solving
1 + -5w = 0

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

Add '-1' to each side of the equation.
1 + -1 + -5w = 0 + -1

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

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

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

Simplifying
w = 0.2
Solution
w = {0.1666666667, 0.2}