10q^2+9q+2=0

Solution for 10q^2+9q+2=0 equation:

Simplifying
10q2 + 9q + 2 = 0

Reorder the terms:
2 + 9q + 10q2 = 0

Solving
2 + 9q + 10q2 = 0

Solving for variable 'q'.

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

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

Simplifying
2 + 5q = 0

Solving
2 + 5q = 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 + 5q = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 5q = 0 + -2
5q = 0 + -2

Combine like terms: 0 + -2 = -2
5q = -2

Divide each side by '5'.
q = -0.4

Simplifying
q = -0.4
Solution
q = {-0.5, -0.4}