9k^2+53k+40=0

Solution for 9k^2+53k+40=0 equation:

Simplifying
9k2 + 53k + 40 = 0

Reorder the terms:
40 + 53k + 9k2 = 0

Solving
40 + 53k + 9k2 = 0

Solving for variable 'k'.

Factor a trinomial.
(5 + k)(8 + 9k) = 0

Subproblem 1
Set the factor '(5 + k)' equal to zero and attempt to solve:

Simplifying
5 + k = 0

Solving
5 + k = 0

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

Add '-5' to each side of the equation.
5 + -5 + k = 0 + -5

Combine like terms: 5 + -5 = 0
0 + k = 0 + -5
k = 0 + -5

Combine like terms: 0 + -5 = -5
k = -5

Simplifying
k = -5
Subproblem 2
Set the factor '(8 + 9k)' equal to zero and attempt to solve:

Simplifying
8 + 9k = 0

Solving
8 + 9k = 0

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

Add '-8' to each side of the equation.
8 + -8 + 9k = 0 + -8

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

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

Divide each side by '9'.
k = -0.8888888889

Simplifying
k = -0.8888888889
Solution
k = {-5, -0.8888888889}