16z^2-10z+1=0

Solution for 16z^2-10z+1=0 equation:

Simplifying
16z2 + -10z + 1 = 0

Reorder the terms:
1 + -10z + 16z2 = 0

Solving
1 + -10z + 16z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(1 + -8z)(1 + -2z) = 0

Subproblem 1
Set the factor '(1 + -8z)' equal to zero and attempt to solve:

Simplifying
1 + -8z = 0

Solving
1 + -8z = 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 + -8z = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -8z = 0 + -1
-8z = 0 + -1

Combine like terms: 0 + -1 = -1
-8z = -1

Divide each side by '-8'.
z = 0.125

Simplifying
z = 0.125
Subproblem 2
Set the factor '(1 + -2z)' equal to zero and attempt to solve:

Simplifying
1 + -2z = 0

Solving
1 + -2z = 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 + -2z = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2z = 0 + -1
-2z = 0 + -1

Combine like terms: 0 + -1 = -1
-2z = -1

Divide each side by '-2'.
z = 0.5

Simplifying
z = 0.5
Solution
z = {0.125, 0.5}