4s^2-5s+1=0

Solution for 4s^2-5s+1=0 equation:

Simplifying
4s2 + -5s + 1 = 0

Reorder the terms:
1 + -5s + 4s2 = 0

Solving
1 + -5s + 4s2 = 0

Solving for variable 's'.

Factor a trinomial.
(1 + -4s)(1 + -1s) = 0

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

Simplifying
1 + -4s = 0

Solving
1 + -4s = 0

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

Add '-1' to each side of the equation.
1 + -1 + -4s = 0 + -1

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

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

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

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

Simplifying
1 + -1s = 0

Solving
1 + -1s = 0

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

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

Combine like terms: 1 + -1 = 0
0 + -1s = 0 + -1
-1s = 0 + -1

Combine like terms: 0 + -1 = -1
-1s = -1

Divide each side by '-1'.
s = 1

Simplifying
s = 1
Solution
s = {0.25, 1}