10r^2+19r+6=0

Solution for 10r^2+19r+6=0 equation:

Simplifying
10r2 + 19r + 6 = 0

Reorder the terms:
6 + 19r + 10r2 = 0

Solving
6 + 19r + 10r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(3 + 2r)(2 + 5r) = 0

Subproblem 1
Set the factor '(3 + 2r)' equal to zero and attempt to solve:

Simplifying
3 + 2r = 0

Solving
3 + 2r = 0

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

Add '-3' to each side of the equation.
3 + -3 + 2r = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2r = 0 + -3
2r = 0 + -3

Combine like terms: 0 + -3 = -3
2r = -3

Divide each side by '2'.
r = -1.5

Simplifying
r = -1.5
Subproblem 2
Set the factor '(2 + 5r)' equal to zero and attempt to solve:

Simplifying
2 + 5r = 0

Solving
2 + 5r = 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 + 5r = 0 + -2

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

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

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

Simplifying
r = -0.4
Solution
r = {-1.5, -0.4}