(3r+3)(6r+1)=0

Solution for (3r+3)(6r+1)=0 equation:

Simplifying
(3r + 3)(6r + 1) = 0

Reorder the terms:
(3 + 3r)(6r + 1) = 0

Reorder the terms:
(3 + 3r)(1 + 6r) = 0

Multiply (3 + 3r) * (1 + 6r)
(3(1 + 6r) + 3r * (1 + 6r)) = 0
((1 * 3 + 6r * 3) + 3r * (1 + 6r)) = 0
((3 + 18r) + 3r * (1 + 6r)) = 0
(3 + 18r + (1 * 3r + 6r * 3r)) = 0
(3 + 18r + (3r + 18r2)) = 0

Combine like terms: 18r + 3r = 21r
(3 + 21r + 18r2) = 0

Solving
3 + 21r + 18r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '3'.
3(1 + 7r + 6r2) = 0

Factor a trinomial.
3((1 + r)(1 + 6r)) = 0

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

Simplifying
1 + r = 0

Solving
1 + r = 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 + r = 0 + -1

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

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

Simplifying
r = -1
Subproblem 2
Set the factor '(1 + 6r)' equal to zero and attempt to solve:

Simplifying
1 + 6r = 0

Solving
1 + 6r = 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 + 6r = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 6r = 0 + -1
6r = 0 + -1

Combine like terms: 0 + -1 = -1
6r = -1

Divide each side by '6'.
r = -0.1666666667

Simplifying
r = -0.1666666667
Solution
r = {-1, -0.1666666667}