(k+5)(k+1)=21

Solution for (k+5)(k+1)=21 equation:

Simplifying
(k + 5)(k + 1) = 21

Reorder the terms:
(5 + k)(k + 1) = 21

Reorder the terms:
(5 + k)(1 + k) = 21

Multiply (5 + k) * (1 + k)
(5(1 + k) + k(1 + k)) = 21
((1 * 5 + k * 5) + k(1 + k)) = 21
((5 + 5k) + k(1 + k)) = 21
(5 + 5k + (1 * k + k * k)) = 21
(5 + 5k + (1k + k2)) = 21

Combine like terms: 5k + 1k = 6k
(5 + 6k + k2) = 21

Solving
5 + 6k + k2 = 21

Solving for variable 'k'.

Reorder the terms:
5 + -21 + 6k + k2 = 21 + -21

Combine like terms: 5 + -21 = -16
-16 + 6k + k2 = 21 + -21

Combine like terms: 21 + -21 = 0
-16 + 6k + k2 = 0

Factor a trinomial.
(-8 + -1k)(2 + -1k) = 0

Subproblem 1
Set the factor '(-8 + -1k)' equal to zero and attempt to solve:

Simplifying
-8 + -1k = 0

Solving
-8 + -1k = 0

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

Add '8' to each side of the equation.
-8 + 8 + -1k = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1k = 0 + 8
-1k = 0 + 8

Combine like terms: 0 + 8 = 8
-1k = 8

Divide each side by '-1'.
k = -8

Simplifying
k = -8
Subproblem 2
Set the factor '(2 + -1k)' equal to zero and attempt to solve:

Simplifying
2 + -1k = 0

Solving
2 + -1k = 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 + -1k = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1k = 0 + -2
-1k = 0 + -2

Combine like terms: 0 + -2 = -2
-1k = -2

Divide each side by '-1'.
k = 2

Simplifying
k = 2
Solution
k = {-8, 2}