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

Solution for (5k+4)(k+1)=0 equation:

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

Reorder the terms:
(4 + 5k)(k + 1) = 0

Reorder the terms:
(4 + 5k)(1 + k) = 0

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

Combine like terms: 4k + 5k = 9k
(4 + 9k + 5k2) = 0

Solving
4 + 9k + 5k2 = 0

Solving for variable 'k'.

Factor a trinomial.
(1 + k)(4 + 5k) = 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 '(4 + 5k)' equal to zero and attempt to solve:

Simplifying
4 + 5k = 0

Solving
4 + 5k = 0

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

Add '-4' to each side of the equation.
4 + -4 + 5k = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 5k = 0 + -4
5k = 0 + -4

Combine like terms: 0 + -4 = -4
5k = -4

Divide each side by '5'.
k = -0.8

Simplifying
k = -0.8
Solution
k = {-1, -0.8}