4y(8y-1)=1

Solution for 4y(8y-1)=1 equation:

Simplifying
4y(8y + -1) = 1

Reorder the terms:
4y(-1 + 8y) = 1
(-1 * 4y + 8y * 4y) = 1
(-4y + 32y2) = 1

Solving
-4y + 32y2 = 1

Solving for variable 'y'.

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

Combine like terms: 1 + -1 = 0
-1 + -4y + 32y2 = 0

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}