9r^2+19r+2=0

Solution for 9r^2+19r+2=0 equation:

Simplifying
9r2 + 19r + 2 = 0

Reorder the terms:
2 + 19r + 9r2 = 0

Solving
2 + 19r + 9r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(2 + r)(1 + 9r) = 0

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

Simplifying
2 + r = 0

Solving
2 + r = 0

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

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

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

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

Simplifying
r = -2
Subproblem 2
Set the factor '(1 + 9r)' equal to zero and attempt to solve:

Simplifying
1 + 9r = 0

Solving
1 + 9r = 0

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

Add '-1' to each side of the equation.
1 + -1 + 9r = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 9r = 0 + -1
9r = 0 + -1

Combine like terms: 0 + -1 = -1
9r = -1

Divide each side by '9'.
r = -0.1111111111

Simplifying
r = -0.1111111111
Solution
r = {-2, -0.1111111111}