r^2+3r+6r+18=0

Solution for r^2+3r+6r+18=0 equation:

Simplifying
r2 + 3r + 6r + 18 = 0

Reorder the terms:
18 + 3r + 6r + r2 = 0

Combine like terms: 3r + 6r = 9r
18 + 9r + r2 = 0

Solving
18 + 9r + r2 = 0

Solving for variable 'r'.

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

Subproblem 1
Set the factor '(6 + r)' equal to zero and attempt to solve:

Simplifying
6 + r = 0

Solving
6 + r = 0

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

Add '-6' to each side of the equation.
6 + -6 + r = 0 + -6

Combine like terms: 6 + -6 = 0
0 + r = 0 + -6
r = 0 + -6

Combine like terms: 0 + -6 = -6
r = -6

Simplifying
r = -6
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 = {-6, -3}