16k^2+8k+1=0

Solution for 16k^2+8k+1=0 equation:

Simplifying
16k2 + 8k + 1 = 0

Reorder the terms:
1 + 8k + 16k2 = 0

Solving
1 + 8k + 16k2 = 0

Solving for variable 'k'.

Factor a trinomial.
(1 + 4k)(1 + 4k) = 0

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

Simplifying
1 + 4k = 0

Solving
1 + 4k = 0

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

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

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

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

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

Simplifying
k = -0.25
Subproblem 2
Set the factor '(1 + 4k)' equal to zero and attempt to solve:

Simplifying
1 + 4k = 0

Solving
1 + 4k = 0

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

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

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

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

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

Simplifying
k = -0.25
Solution
k = {-0.25, -0.25}