2q^2+9q+4=0

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

Simplifying
2q2 + 9q + 4 = 0

Reorder the terms:
4 + 9q + 2q2 = 0

Solving
4 + 9q + 2q2 = 0

Solving for variable 'q'.

Factor a trinomial.
(4 + q)(1 + 2q) = 0

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

Simplifying
4 + q = 0

Solving
4 + q = 0

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

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

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

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

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

Simplifying
1 + 2q = 0

Solving
1 + 2q = 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 + 2q = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2q = 0 + -1
2q = 0 + -1

Combine like terms: 0 + -1 = -1
2q = -1

Divide each side by '2'.
q = -0.5

Simplifying
q = -0.5
Solution
q = {-4, -0.5}