4q^2+9q+5=0

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

Simplifying
4q2 + 9q + 5 = 0

Reorder the terms:
5 + 9q + 4q2 = 0

Solving
5 + 9q + 4q2 = 0

Solving for variable 'q'.

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

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

Simplifying
5 + 4q = 0

Solving
5 + 4q = 0

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

Add '-5' to each side of the equation.
5 + -5 + 4q = 0 + -5

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

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

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

Simplifying
q = -1.25
Subproblem 2
Set the factor '(1 + q)' equal to zero and attempt to solve:

Simplifying
1 + q = 0

Solving
1 + q = 0

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

Add '-1' to each side of the equation.
1 + -1 + q = 0 + -1

Combine like terms: 1 + -1 = 0
0 + q = 0 + -1
q = 0 + -1

Combine like terms: 0 + -1 = -1
q = -1

Simplifying
q = -1
Solution
q = {-1.25, -1}