(r+9)(r-12)=0

Solution for (r+9)(r-12)=0 equation:

Simplifying
(r + 9)(r + -12) = 0

Reorder the terms:
(9 + r)(r + -12) = 0

Reorder the terms:
(9 + r)(-12 + r) = 0

Multiply (9 + r) * (-12 + r)
(9(-12 + r) + r(-12 + r)) = 0
((-12 * 9 + r * 9) + r(-12 + r)) = 0
((-108 + 9r) + r(-12 + r)) = 0
(-108 + 9r + (-12 * r + r * r)) = 0
(-108 + 9r + (-12r + r2)) = 0

Combine like terms: 9r + -12r = -3r
(-108 + -3r + r2) = 0

Solving
-108 + -3r + r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(-9 + -1r)(12 + -1r) = 0

Subproblem 1
Set the factor '(-9 + -1r)' equal to zero and attempt to solve:

Simplifying
-9 + -1r = 0

Solving
-9 + -1r = 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 + -1r = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -1r = 0 + 9
-1r = 0 + 9

Combine like terms: 0 + 9 = 9
-1r = 9

Divide each side by '-1'.
r = -9

Simplifying
r = -9
Subproblem 2
Set the factor '(12 + -1r)' equal to zero and attempt to solve:

Simplifying
12 + -1r = 0

Solving
12 + -1r = 0

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

Add '-12' to each side of the equation.
12 + -12 + -1r = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -1r = 0 + -12
-1r = 0 + -12

Combine like terms: 0 + -12 = -12
-1r = -12

Divide each side by '-1'.
r = 12

Simplifying
r = 12
Solution
r = {-9, 12}