-8w^2+6w-1=0

Solution for -8w^2+6w-1=0 equation:

Simplifying
-8w2 + 6w + -1 = 0

Reorder the terms:
-1 + 6w + -8w2 = 0

Solving
-1 + 6w + -8w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(-1 + 2w)(1 + -4w) = 0

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

Simplifying
-1 + 2w = 0

Solving
-1 + 2w = 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 + 2w = 0 + 1

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

Combine like terms: 0 + 1 = 1
2w = 1

Divide each side by '2'.
w = 0.5

Simplifying
w = 0.5
Subproblem 2
Set the factor '(1 + -4w)' equal to zero and attempt to solve:

Simplifying
1 + -4w = 0

Solving
1 + -4w = 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 + -4w = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -4w = 0 + -1
-4w = 0 + -1

Combine like terms: 0 + -1 = -1
-4w = -1

Divide each side by '-4'.
w = 0.25

Simplifying
w = 0.25
Solution
w = {0.5, 0.25}