4W(8W+1)=1

Solution for 4W(8W+1)=1 equation:

Simplifying
4W(8W + 1) = 1

Reorder the terms:
4W(1 + 8W) = 1
(1 * 4W + 8W * 4W) = 1
(4W + 32W2) = 1

Solving
4W + 32W2 = 1

Solving for variable 'W'.

Reorder the terms:
-1 + 4W + 32W2 = 1 + -1

Combine like terms: 1 + -1 = 0
-1 + 4W + 32W2 = 0

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

Subproblem 1
Set the factor '(-1 + -4W)' equal to zero and attempt to solve:

Simplifying
-1 + -4W = 0

Solving
-1 + -4W = 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 + -4W = 0 + 1

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

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

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

Simplifying
W = -0.25
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 = {-0.25, 0.125}