(2k-1)(4k+3)=0

Solution for (2k-1)(4k+3)=0 equation:

Simplifying
(2k + -1)(4k + 3) = 0

Reorder the terms:
(-1 + 2k)(4k + 3) = 0

Reorder the terms:
(-1 + 2k)(3 + 4k) = 0

Multiply (-1 + 2k) * (3 + 4k)
(-1(3 + 4k) + 2k * (3 + 4k)) = 0
((3 * -1 + 4k * -1) + 2k * (3 + 4k)) = 0
((-3 + -4k) + 2k * (3 + 4k)) = 0
(-3 + -4k + (3 * 2k + 4k * 2k)) = 0
(-3 + -4k + (6k + 8k2)) = 0

Combine like terms: -4k + 6k = 2k
(-3 + 2k + 8k2) = 0

Solving
-3 + 2k + 8k2 = 0

Solving for variable 'k'.

Factor a trinomial.
(-3 + -4k)(1 + -2k) = 0

Subproblem 1
Set the factor '(-3 + -4k)' equal to zero and attempt to solve:

Simplifying
-3 + -4k = 0

Solving
-3 + -4k = 0

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

Add '3' to each side of the equation.
-3 + 3 + -4k = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -4k = 0 + 3
-4k = 0 + 3

Combine like terms: 0 + 3 = 3
-4k = 3

Divide each side by '-4'.
k = -0.75

Simplifying
k = -0.75
Subproblem 2
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
Solution
k = {-0.75, 0.5}