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

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

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

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

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

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

Combine like terms: 5k + -1k = 4k
(-5 + 4k + k2) = -8

Solving
-5 + 4k + k2 = -8

Solving for variable 'k'.

Reorder the terms:
-5 + 8 + 4k + k2 = -8 + 8

Combine like terms: -5 + 8 = 3
3 + 4k + k2 = -8 + 8

Combine like terms: -8 + 8 = 0
3 + 4k + k2 = 0

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

Subproblem 1
Set the factor '(3 + k)' equal to zero and attempt to solve:

Simplifying
3 + k = 0

Solving
3 + k = 0

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

Add '-3' to each side of the equation.
3 + -3 + k = 0 + -3

Combine like terms: 3 + -3 = 0
0 + k = 0 + -3
k = 0 + -3

Combine like terms: 0 + -3 = -3
k = -3

Simplifying
k = -3
Subproblem 2
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
Solution
k = {-3, -1}