4k(k+1)+8(k+1)=

Solution for 4k(k+1)+8(k+1)= equation:

Simplifying
4k(k + 1) + 8(k + 1) = 0

Reorder the terms:
4k(1 + k) + 8(k + 1) = 0
(1 * 4k + k * 4k) + 8(k + 1) = 0
(4k + 4k2) + 8(k + 1) = 0

Reorder the terms:
4k + 4k2 + 8(1 + k) = 0
4k + 4k2 + (1 * 8 + k * 8) = 0
4k + 4k2 + (8 + 8k) = 0

Reorder the terms:
8 + 4k + 8k + 4k2 = 0

Combine like terms: 4k + 8k = 12k
8 + 12k + 4k2 = 0

Solving
8 + 12k + 4k2 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), '4'.
4(2 + 3k + k2) = 0

Factor a trinomial.
4((2 + k)(1 + k)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(2 + k)' equal to zero and attempt to solve:

Simplifying
2 + k = 0

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

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

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

Simplifying
k = -2
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 = {-2, -1}