6w^2-7w+1=0

Solution for 6w^2-7w+1=0 equation:

Simplifying
6w2 + -7w + 1 = 0

Reorder the terms:
1 + -7w + 6w2 = 0

Solving
1 + -7w + 6w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(1 + -6w)(1 + -1w) = 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 + -1w)' equal to zero and attempt to solve:

Simplifying
1 + -1w = 0

Solving
1 + -1w = 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 + -1w = 0 + -1

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

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

Divide each side by '-1'.
w = 1

Simplifying
w = 1
Solution
w = {0.1666666667, 1}