16w^2+6w-1=0

Solution for 16w^2+6w-1=0 equation:

Simplifying
16w2 + 6w + -1 = 0

Reorder the terms:
-1 + 6w + 16w2 = 0

Solving
-1 + 6w + 16w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(-1 + -2w)(1 + -8w) = 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 + -8w)' equal to zero and attempt to solve:

Simplifying
1 + -8w = 0

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

Combine like terms: 1 + -1 = 0
0 + -8w = 0 + -1
-8w = 0 + -1

Combine like terms: 0 + -1 = -1
-8w = -1

Divide each side by '-8'.
w = 0.125

Simplifying
w = 0.125
Solution
w = {-0.5, 0.125}