If you question is how to factor it, you aready did.
If the question is the value of w, it is best to rewrite in standard polynomial equation form first.
8w^2 + 2x -1 = 0
(4x -1)(2x +1) = 0
x = 1/4 or -1/2
2w(4w+1)=1
2 answers
thank you yes i was trying to figure out how to solve for w