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

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

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

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

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

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

Combine like terms: -1k + 4k = 3k
(-1 + 3k + 4k2) = 0

Solving
-1 + 3k + 4k2 = 0

Solving for variable 'k'.

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

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

Simplifying
-1 + -1k = 0

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

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

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

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

Simplifying
k = -1
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 = {-1, 0.25}