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

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

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

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

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

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

Combine like terms: 27r + 27r = 54r
(81 + 54r + 9r2) = 0

Solving
81 + 54r + 9r2 = 0

Solving for variable 'r'.

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

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

Ignore the factor 9.
Subproblem 1
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
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, -3}