4k^2+29k+45=0

Solution for 4k^2+29k+45=0 equation:

Simplifying
4k2 + 29k + 45 = 0

Reorder the terms:
45 + 29k + 4k2 = 0

Solving
45 + 29k + 4k2 = 0

Solving for variable 'k'.

Factor a trinomial.
(5 + k)(9 + 4k) = 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 '(9 + 4k)' equal to zero and attempt to solve:

Simplifying
9 + 4k = 0

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

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

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

Divide each side by '4'.
k = -2.25

Simplifying
k = -2.25
Solution
k = {-5, -2.25}