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

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

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

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

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

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

Combine like terms: -18r + 6r = -12r
(-18 + -12r + 6r2) = 0

Solving
-18 + -12r + 6r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-3 + -2r + r2) = 0

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

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

Simplifying
-1 + -1r = 0

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

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

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

Divide each side by '-1'.
r = -1

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

Simplifying
3 + -1r = 0

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

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

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

Divide each side by '-1'.
r = 3

Simplifying
r = 3
Solution
r = {-1, 3}