k^2+2k=-8k-24

Solution for k^2+2k=-8k-24 equation:

Simplifying
k2 + 2k = -8k + -24

Reorder the terms:
2k + k2 = -8k + -24

Reorder the terms:
2k + k2 = -24 + -8k

Solving
2k + k2 = -24 + -8k

Solving for variable 'k'.

Reorder the terms:
24 + 2k + 8k + k2 = -24 + -8k + 24 + 8k

Combine like terms: 2k + 8k = 10k
24 + 10k + k2 = -24 + -8k + 24 + 8k

Reorder the terms:
24 + 10k + k2 = -24 + 24 + -8k + 8k

Combine like terms: -24 + 24 = 0
24 + 10k + k2 = 0 + -8k + 8k
24 + 10k + k2 = -8k + 8k

Combine like terms: -8k + 8k = 0
24 + 10k + k2 = 0

Factor a trinomial.
(6 + k)(4 + k) = 0

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

Simplifying
6 + k = 0

Solving
6 + k = 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 + k = 0 + -6

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

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

Simplifying
k = -6
Subproblem 2
Set the factor '(4 + k)' equal to zero and attempt to solve:

Simplifying
4 + k = 0

Solving
4 + k = 0

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

Add '-4' to each side of the equation.
4 + -4 + k = 0 + -4

Combine like terms: 4 + -4 = 0
0 + k = 0 + -4
k = 0 + -4

Combine like terms: 0 + -4 = -4
k = -4

Simplifying
k = -4
Solution
k = {-6, -4}