(2r+9)(9r+3)=0

Solution for (2r+9)(9r+3)=0 equation:

Simplifying
(2r + 9)(9r + 3) = 0

Reorder the terms:
(9 + 2r)(9r + 3) = 0

Reorder the terms:
(9 + 2r)(3 + 9r) = 0

Multiply (9 + 2r) * (3 + 9r)
(9(3 + 9r) + 2r * (3 + 9r)) = 0
((3 * 9 + 9r * 9) + 2r * (3 + 9r)) = 0
((27 + 81r) + 2r * (3 + 9r)) = 0
(27 + 81r + (3 * 2r + 9r * 2r)) = 0
(27 + 81r + (6r + 18r2)) = 0

Combine like terms: 81r + 6r = 87r
(27 + 87r + 18r2) = 0

Solving
27 + 87r + 18r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '3'.
3(9 + 29r + 6r2) = 0

Factor a trinomial.
3((9 + 2r)(1 + 3r)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(9 + 2r)' equal to zero and attempt to solve:

Simplifying
9 + 2r = 0

Solving
9 + 2r = 0

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

Add '-9' to each side of the equation.
9 + -9 + 2r = 0 + -9

Combine like terms: 9 + -9 = 0
0 + 2r = 0 + -9
2r = 0 + -9

Combine like terms: 0 + -9 = -9
2r = -9

Divide each side by '2'.
r = -4.5

Simplifying
r = -4.5
Subproblem 2
Set the factor '(1 + 3r)' equal to zero and attempt to solve:

Simplifying
1 + 3r = 0

Solving
1 + 3r = 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 + 3r = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 3r = 0 + -1
3r = 0 + -1

Combine like terms: 0 + -1 = -1
3r = -1

Divide each side by '3'.
r = -0.3333333333

Simplifying
r = -0.3333333333
Solution
r = {-4.5, -0.3333333333}