144k^2+24k+1=0

Solution for 144k^2+24k+1=0 equation:

Simplifying
144k2 + 24k + 1 = 0

Reorder the terms:
1 + 24k + 144k2 = 0

Solving
1 + 24k + 144k2 = 0

Solving for variable 'k'.

Factor a trinomial.
(1 + 12k)(1 + 12k) = 0

Subproblem 1
Set the factor '(1 + 12k)' equal to zero and attempt to solve:

Simplifying
1 + 12k = 0

Solving
1 + 12k = 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 + 12k = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 12k = 0 + -1
12k = 0 + -1

Combine like terms: 0 + -1 = -1
12k = -1

Divide each side by '12'.
k = -0.08333333333

Simplifying
k = -0.08333333333
Subproblem 2
Set the factor '(1 + 12k)' equal to zero and attempt to solve:

Simplifying
1 + 12k = 0

Solving
1 + 12k = 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 + 12k = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 12k = 0 + -1
12k = 0 + -1

Combine like terms: 0 + -1 = -1
12k = -1

Divide each side by '12'.
k = -0.08333333333

Simplifying
k = -0.08333333333
Solution
k = {-0.08333333333, -0.08333333333}