(5k+2)(k+1)=0

Solution for (5k+2)(k+1)=0 equation:

Simplifying
(5k + 2)(k + 1) = 0

Reorder the terms:
(2 + 5k)(k + 1) = 0

Reorder the terms:
(2 + 5k)(1 + k) = 0

Multiply (2 + 5k) * (1 + k)
(2(1 + k) + 5k * (1 + k)) = 0
((1 * 2 + k * 2) + 5k * (1 + k)) = 0
((2 + 2k) + 5k * (1 + k)) = 0
(2 + 2k + (1 * 5k + k * 5k)) = 0
(2 + 2k + (5k + 5k2)) = 0

Combine like terms: 2k + 5k = 7k
(2 + 7k + 5k2) = 0

Solving
2 + 7k + 5k2 = 0

Solving for variable 'k'.

Factor a trinomial.
(1 + k)(2 + 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 '(2 + 5k)' equal to zero and attempt to solve:

Simplifying
2 + 5k = 0

Solving
2 + 5k = 0

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

Add '-2' to each side of the equation.
2 + -2 + 5k = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 5k = 0 + -2
5k = 0 + -2

Combine like terms: 0 + -2 = -2
5k = -2

Divide each side by '5'.
k = -0.4

Simplifying
k = -0.4
Solution
k = {-1, -0.4}