(2k+1)(4k-1)=0

Solution for (2k+1)(4k-1)=0 equation:

Simplifying
(2k + 1)(4k + -1) = 0

Reorder the terms:
(1 + 2k)(4k + -1) = 0

Reorder the terms:
(1 + 2k)(-1 + 4k) = 0

Multiply (1 + 2k) * (-1 + 4k)
(1(-1 + 4k) + 2k * (-1 + 4k)) = 0
((-1 * 1 + 4k * 1) + 2k * (-1 + 4k)) = 0
((-1 + 4k) + 2k * (-1 + 4k)) = 0
(-1 + 4k + (-1 * 2k + 4k * 2k)) = 0
(-1 + 4k + (-2k + 8k2)) = 0

Combine like terms: 4k + -2k = 2k
(-1 + 2k + 8k2) = 0

Solving
-1 + 2k + 8k2 = 0

Solving for variable 'k'.

Factor a trinomial.
(-1 + -2k)(1 + -4k) = 0

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

Simplifying
-1 + -2k = 0

Solving
-1 + -2k = 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 + -2k = 0 + 1

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

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

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

Simplifying
k = -0.5
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 = {-0.5, 0.25}