-9w^2-8w+1=0

Solution for -9w^2-8w+1=0 equation:

Simplifying
-9w2 + -8w + 1 = 0

Reorder the terms:
1 + -8w + -9w2 = 0

Solving
1 + -8w + -9w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(1 + -9w)(1 + w) = 0

Subproblem 1
Set the factor '(1 + -9w)' equal to zero and attempt to solve:

Simplifying
1 + -9w = 0

Solving
1 + -9w = 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 + -9w = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -9w = 0 + -1
-9w = 0 + -1

Combine like terms: 0 + -1 = -1
-9w = -1

Divide each side by '-9'.
w = 0.1111111111

Simplifying
w = 0.1111111111
Subproblem 2
Set the factor '(1 + w)' equal to zero and attempt to solve:

Simplifying
1 + w = 0

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

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

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

Simplifying
w = -1
Solution
w = {0.1111111111, -1}