k^2+9k+10=-8

Solution for k^2+9k+10=-8 equation:

Simplifying
k2 + 9k + 10 = -8

Reorder the terms:
10 + 9k + k2 = -8

Solving
10 + 9k + k2 = -8

Solving for variable 'k'.

Reorder the terms:
10 + 8 + 9k + k2 = -8 + 8

Combine like terms: 10 + 8 = 18
18 + 9k + k2 = -8 + 8

Combine like terms: -8 + 8 = 0
18 + 9k + k2 = 0

Factor a trinomial.
(6 + k)(3 + 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 '(3 + k)' equal to zero and attempt to solve:

Simplifying
3 + k = 0

Solving
3 + k = 0

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

Add '-3' to each side of the equation.
3 + -3 + k = 0 + -3

Combine like terms: 3 + -3 = 0
0 + k = 0 + -3
k = 0 + -3

Combine like terms: 0 + -3 = -3
k = -3

Simplifying
k = -3
Solution
k = {-6, -3}