5q^2+16q+11=0

Solution for 5q^2+16q+11=0 equation:

Simplifying
5q2 + 16q + 11 = 0

Reorder the terms:
11 + 16q + 5q2 = 0

Solving
11 + 16q + 5q2 = 0

Solving for variable 'q'.

Factor a trinomial.
(11 + 5q)(1 + q) = 0

Subproblem 1
Set the factor '(11 + 5q)' equal to zero and attempt to solve:

Simplifying
11 + 5q = 0

Solving
11 + 5q = 0

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

Add '-11' to each side of the equation.
11 + -11 + 5q = 0 + -11

Combine like terms: 11 + -11 = 0
0 + 5q = 0 + -11
5q = 0 + -11

Combine like terms: 0 + -11 = -11
5q = -11

Divide each side by '5'.
q = -2.2

Simplifying
q = -2.2
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 = {-2.2, -1}