(9k^2+22k+8)=0

Solution for (9k^2+22k+8)=0 equation:

Simplifying
(9k2 + 22k + 8) = 0

Reorder the terms:
(8 + 22k + 9k2) = 0

Remove parenthesis around (8 + 22k + 9k2)
8 + 22k + 9k2 = 0

Solving
8 + 22k + 9k2 = 0

Solving for variable 'k'.

Factor a trinomial.
(2 + k)(4 + 9k) = 0

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 '(4 + 9k)' equal to zero and attempt to solve:

Simplifying
4 + 9k = 0

Solving
4 + 9k = 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 + 9k = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 9k = 0 + -4
9k = 0 + -4

Combine like terms: 0 + -4 = -4
9k = -4

Divide each side by '9'.
k = -0.4444444444

Simplifying
k = -0.4444444444
Solution
k = {-2, -0.4444444444}