10q^2+11q+1=0

Solution for 10q^2+11q+1=0 equation:

Simplifying
10q2 + 11q + 1 = 0

Reorder the terms:
1 + 11q + 10q2 = 0

Solving
1 + 11q + 10q2 = 0

Solving for variable 'q'.

Factor a trinomial.
(1 + q)(1 + 10q) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(1 + 10q)' equal to zero and attempt to solve:

Simplifying
1 + 10q = 0

Solving
1 + 10q = 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 + 10q = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 10q = 0 + -1
10q = 0 + -1

Combine like terms: 0 + -1 = -1
10q = -1

Divide each side by '10'.
q = -0.1

Simplifying
q = -0.1
Solution
q = {-1, -0.1}