(r-8)(3r+9)=0

Solution for (r-8)(3r+9)=0 equation:

Simplifying
(r + -8)(3r + 9) = 0

Reorder the terms:
(-8 + r)(3r + 9) = 0

Reorder the terms:
(-8 + r)(9 + 3r) = 0

Multiply (-8 + r) * (9 + 3r)
(-8(9 + 3r) + r(9 + 3r)) = 0
((9 * -8 + 3r * -8) + r(9 + 3r)) = 0
((-72 + -24r) + r(9 + 3r)) = 0
(-72 + -24r + (9 * r + 3r * r)) = 0
(-72 + -24r + (9r + 3r2)) = 0

Combine like terms: -24r + 9r = -15r
(-72 + -15r + 3r2) = 0

Solving
-72 + -15r + 3r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-24 + -5r + r2) = 0

Factor a trinomial.
3((-3 + -1r)(8 + -1r)) = 0

Ignore the factor 3.
Subproblem 1
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
Subproblem 2
Set the factor '(8 + -1r)' equal to zero and attempt to solve:

Simplifying
8 + -1r = 0

Solving
8 + -1r = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1r = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1r = 0 + -8
-1r = 0 + -8

Combine like terms: 0 + -8 = -8
-1r = -8

Divide each side by '-1'.
r = 8

Simplifying
r = 8
Solution
r = {-3, 8}