36z^2+13z+1=0

Solution for 36z^2+13z+1=0 equation:

Simplifying
36z2 + 13z + 1 = 0

Reorder the terms:
1 + 13z + 36z2 = 0

Solving
1 + 13z + 36z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(1 + 4z)(1 + 9z) = 0

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

Simplifying
1 + 4z = 0

Solving
1 + 4z = 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 + 4z = 0 + -1

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

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

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

Simplifying
z = -0.25
Subproblem 2
Set the factor '(1 + 9z)' equal to zero and attempt to solve:

Simplifying
1 + 9z = 0

Solving
1 + 9z = 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 + 9z = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 9z = 0 + -1
9z = 0 + -1

Combine like terms: 0 + -1 = -1
9z = -1

Divide each side by '9'.
z = -0.1111111111

Simplifying
z = -0.1111111111
Solution
z = {-0.25, -0.1111111111}