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

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

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

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

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

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

Combine like terms: 1k + -5k = -4k
(-5 + -4k + k2) = 0

Solving
-5 + -4k + k2 = 0

Solving for variable 'k'.

Factor a trinomial.
(-1 + -1k)(5 + -1k) = 0

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

Simplifying
-1 + -1k = 0

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

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

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

Divide each side by '-1'.
k = -1

Simplifying
k = -1
Subproblem 2
Set the factor '(5 + -1k)' equal to zero and attempt to solve:

Simplifying
5 + -1k = 0

Solving
5 + -1k = 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 + -1k = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1k = 0 + -5
-1k = 0 + -5

Combine like terms: 0 + -5 = -5
-1k = -5

Divide each side by '-1'.
k = 5

Simplifying
k = 5
Solution
k = {-1, 5}