(k+4)(k+1)=10

Solution for (k+4)(k+1)=10 equation:

Simplifying
(k + 4)(k + 1) = 10

Reorder the terms:
(4 + k)(k + 1) = 10

Reorder the terms:
(4 + k)(1 + k) = 10

Multiply (4 + k) * (1 + k)
(4(1 + k) + k(1 + k)) = 10
((1 * 4 + k * 4) + k(1 + k)) = 10
((4 + 4k) + k(1 + k)) = 10
(4 + 4k + (1 * k + k * k)) = 10
(4 + 4k + (1k + k2)) = 10

Combine like terms: 4k + 1k = 5k
(4 + 5k + k2) = 10

Solving
4 + 5k + k2 = 10

Solving for variable 'k'.

Reorder the terms:
4 + -10 + 5k + k2 = 10 + -10

Combine like terms: 4 + -10 = -6
-6 + 5k + k2 = 10 + -10

Combine like terms: 10 + -10 = 0
-6 + 5k + k2 = 0

Factor a trinomial.
(-6 + -1k)(1 + -1k) = 0

Subproblem 1
Set the factor '(-6 + -1k)' equal to zero and attempt to solve:

Simplifying
-6 + -1k = 0

Solving
-6 + -1k = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1k = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1k = 0 + 6
-1k = 0 + 6

Combine like terms: 0 + 6 = 6
-1k = 6

Divide each side by '-1'.
k = -6

Simplifying
k = -6
Subproblem 2
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
Solution
k = {-6, 1}