0=36L^2-12L+1

Solution for 0=36L^2-12L+1 equation:

Simplifying
0 = 36L2 + -12L + 1

Reorder the terms:
0 = 1 + -12L + 36L2

Solving
0 = 1 + -12L + 36L2

Solving for variable 'L'.

Combine like terms: 0 + -1 = -1
-1 + 12L + -36L2 = 1 + -12L + 36L2 + -1 + 12L + -36L2

Reorder the terms:
-1 + 12L + -36L2 = 1 + -1 + -12L + 12L + 36L2 + -36L2

Combine like terms: 1 + -1 = 0
-1 + 12L + -36L2 = 0 + -12L + 12L + 36L2 + -36L2
-1 + 12L + -36L2 = -12L + 12L + 36L2 + -36L2

Combine like terms: -12L + 12L = 0
-1 + 12L + -36L2 = 0 + 36L2 + -36L2
-1 + 12L + -36L2 = 36L2 + -36L2

Combine like terms: 36L2 + -36L2 = 0
-1 + 12L + -36L2 = 0

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

Subproblem 1
Set the factor '(-1 + 6L)' equal to zero and attempt to solve:

Simplifying
-1 + 6L = 0

Solving
-1 + 6L = 0

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

Add '1' to each side of the equation.
-1 + 1 + 6L = 0 + 1

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

Combine like terms: 0 + 1 = 1
6L = 1

Divide each side by '6'.
L = 0.1666666667

Simplifying
L = 0.1666666667
Subproblem 2
Set the factor '(1 + -6L)' equal to zero and attempt to solve:

Simplifying
1 + -6L = 0

Solving
1 + -6L = 0

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

Add '-1' to each side of the equation.
1 + -1 + -6L = 0 + -1

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

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

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

Simplifying
L = 0.1666666667
Solution
L = {0.1666666667, 0.1666666667}