9q^2+40q+16=0

Solution for 9q^2+40q+16=0 equation:

Simplifying
9q2 + 40q + 16 = 0

Reorder the terms:
16 + 40q + 9q2 = 0

Solving
16 + 40q + 9q2 = 0

Solving for variable 'q'.

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

Simplifying
4 + 9q = 0

Solving
4 + 9q = 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 + 9q = 0 + -4

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

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

Divide each side by '9'.
q = -0.4444444444

Simplifying
q = -0.4444444444
Solution
q = {-4, -0.4444444444}