36z^2-12z+1=0

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

Simplifying
36z2 + -12z + 1 = 0

Reorder the terms:
1 + -12z + 36z2 = 0

Solving
1 + -12z + 36z2 = 0

Solving for variable 'z'.

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

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

Simplifying
1 + -6z = 0

Solving
1 + -6z = 0

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

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

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

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

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

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

Simplifying
1 + -6z = 0

Solving
1 + -6z = 0

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

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

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

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

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

Simplifying
z = 0.1666666667
Solution
z = {0.1666666667, 0.1666666667}