5q^2+11q+2=0

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

Simplifying
5q2 + 11q + 2 = 0

Reorder the terms:
2 + 11q + 5q2 = 0

Solving
2 + 11q + 5q2 = 0

Solving for variable 'q'.

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

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

Simplifying
2 + q = 0

Solving
2 + q = 0

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

Add '-2' to each side of the equation.
2 + -2 + q = 0 + -2

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

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

Simplifying
q = -2
Subproblem 2
Set the factor '(1 + 5q)' equal to zero and attempt to solve:

Simplifying
1 + 5q = 0

Solving
1 + 5q = 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 + 5q = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 5q = 0 + -1
5q = 0 + -1

Combine like terms: 0 + -1 = -1
5q = -1

Divide each side by '5'.
q = -0.2

Simplifying
q = -0.2
Solution
q = {-2, -0.2}