32y^2-4y-1=0

Solution for 32y^2-4y-1=0 equation:

Simplifying
32y2 + -4y + -1 = 0

Reorder the terms:
-1 + -4y + 32y2 = 0

Solving
-1 + -4y + 32y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(-1 + -8y)(1 + -4y) = 0

Subproblem 1
Set the factor '(-1 + -8y)' equal to zero and attempt to solve:

Simplifying
-1 + -8y = 0

Solving
-1 + -8y = 0

Move all terms containing y to the left, all other terms to the right.

Add '1' to each side of the equation.
-1 + 1 + -8y = 0 + 1

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

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

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

Simplifying
y = -0.125
Subproblem 2
Set the factor '(1 + -4y)' equal to zero and attempt to solve:

Simplifying
1 + -4y = 0

Solving
1 + -4y = 0

Move all terms containing y to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + -4y = 0 + -1

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

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

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

Simplifying
y = 0.25
Solution
y = {-0.125, 0.25}