4k^2+37k+9=0

Solution for 4k^2+37k+9=0 equation:

Simplifying
4k2 + 37k + 9 = 0

Reorder the terms:
9 + 37k + 4k2 = 0

Solving
9 + 37k + 4k2 = 0

Solving for variable 'k'.

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

Subproblem 1
Set the factor '(9 + k)' equal to zero and attempt to solve:

Simplifying
9 + k = 0

Solving
9 + k = 0

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

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

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

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

Simplifying
k = -9
Subproblem 2
Set the factor '(1 + 4k)' equal to zero and attempt to solve:

Simplifying
1 + 4k = 0

Solving
1 + 4k = 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 + 4k = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 4k = 0 + -1
4k = 0 + -1

Combine like terms: 0 + -1 = -1
4k = -1

Divide each side by '4'.
k = -0.25

Simplifying
k = -0.25
Solution
k = {-9, -0.25}