(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 = 5k
(1 + 5k + 4k2) = 0

Solving
1 + 5k + 4k2 = 0

Solving for variable 'k'.

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

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

Simplifying
1 + k = 0

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

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

Combine like terms: 0 + -1 = -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}