3r^2+19r+30=0

Solution for 3r^2+19r+30=0 equation:

Simplifying
3r2 + 19r + 30 = 0

Reorder the terms:
30 + 19r + 3r2 = 0

Solving
30 + 19r + 3r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(10 + 3r)(3 + r) = 0

Subproblem 1
Set the factor '(10 + 3r)' equal to zero and attempt to solve:

Simplifying
10 + 3r = 0

Solving
10 + 3r = 0

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

Add '-10' to each side of the equation.
10 + -10 + 3r = 0 + -10

Combine like terms: 10 + -10 = 0
0 + 3r = 0 + -10
3r = 0 + -10

Combine like terms: 0 + -10 = -10
3r = -10

Divide each side by '3'.
r = -3.333333333

Simplifying
r = -3.333333333
Subproblem 2
Set the factor '(3 + r)' equal to zero and attempt to solve:

Simplifying
3 + r = 0

Solving
3 + r = 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 + r = 0 + -3

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

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

Simplifying
r = -3
Solution
r = {-3.333333333, -3}