4k^2+9k+5=0

Solution for 4k^2+9k+5=0 equation:

Simplifying
4k2 + 9k + 5 = 0

Reorder the terms:
5 + 9k + 4k2 = 0

Solving
5 + 9k + 4k2 = 0

Solving for variable 'k'.

Factor a trinomial.
(5 + 4k)(1 + k) = 0

Subproblem 1
Set the factor '(5 + 4k)' equal to zero and attempt to solve:

Simplifying
5 + 4k = 0

Solving
5 + 4k = 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 + 4k = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 4k = 0 + -5
4k = 0 + -5

Combine like terms: 0 + -5 = -5
4k = -5

Divide each side by '4'.
k = -1.25

Simplifying
k = -1.25
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 = {-1.25, -1}