3w(6w+1)=1

Solution for 3w(6w+1)=1 equation:

Simplifying
3w(6w + 1) = 1

Reorder the terms:
3w(1 + 6w) = 1
(1 * 3w + 6w * 3w) = 1
(3w + 18w2) = 1

Solving
3w + 18w2 = 1

Solving for variable 'w'.

Reorder the terms:
-1 + 3w + 18w2 = 1 + -1

Combine like terms: 1 + -1 = 0
-1 + 3w + 18w2 = 0

Factor a trinomial.
(-1 + -3w)(1 + -6w) = 0

Subproblem 1
Set the factor '(-1 + -3w)' equal to zero and attempt to solve:

Simplifying
-1 + -3w = 0

Solving
-1 + -3w = 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 + -3w = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -3w = 0 + 1
-3w = 0 + 1

Combine like terms: 0 + 1 = 1
-3w = 1

Divide each side by '-3'.
w = -0.3333333333

Simplifying
w = -0.3333333333
Subproblem 2
Set the factor '(1 + -6w)' equal to zero and attempt to solve:

Simplifying
1 + -6w = 0

Solving
1 + -6w = 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 + -6w = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -6w = 0 + -1
-6w = 0 + -1

Combine like terms: 0 + -1 = -1
-6w = -1

Divide each side by '-6'.
w = 0.1666666667

Simplifying
w = 0.1666666667
Solution
w = {-0.3333333333, 0.1666666667}