(8k+5)(k+1)=0

Solution for (8k+5)(k+1)=0 equation:

Simplifying
(8k + 5)(k + 1) = 0

Reorder the terms:
(5 + 8k)(k + 1) = 0

Reorder the terms:
(5 + 8k)(1 + k) = 0

Multiply (5 + 8k) * (1 + k)
(5(1 + k) + 8k * (1 + k)) = 0
((1 * 5 + k * 5) + 8k * (1 + k)) = 0
((5 + 5k) + 8k * (1 + k)) = 0
(5 + 5k + (1 * 8k + k * 8k)) = 0
(5 + 5k + (8k + 8k2)) = 0

Combine like terms: 5k + 8k = 13k
(5 + 13k + 8k2) = 0

Solving
5 + 13k + 8k2 = 0

Solving for variable 'k'.

Factor a trinomial.
(1 + k)(5 + 8k) = 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 '(5 + 8k)' equal to zero and attempt to solve:

Simplifying
5 + 8k = 0

Solving
5 + 8k = 0

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

Add '-5' to each side of the equation.
5 + -5 + 8k = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 8k = 0 + -5
8k = 0 + -5

Combine like terms: 0 + -5 = -5
8k = -5

Divide each side by '8'.
k = -0.625

Simplifying
k = -0.625
Solution
k = {-1, -0.625}