(r-9)(r+36)=0

Solution for (r-9)(r+36)=0 equation:

Simplifying
(r + -9)(r + 36) = 0

Reorder the terms:
(-9 + r)(r + 36) = 0

Reorder the terms:
(-9 + r)(36 + r) = 0

Multiply (-9 + r) * (36 + r)
(-9(36 + r) + r(36 + r)) = 0
((36 * -9 + r * -9) + r(36 + r)) = 0
((-324 + -9r) + r(36 + r)) = 0
(-324 + -9r + (36 * r + r * r)) = 0
(-324 + -9r + (36r + r2)) = 0

Combine like terms: -9r + 36r = 27r
(-324 + 27r + r2) = 0

Solving
-324 + 27r + r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(-36 + -1r)(9 + -1r) = 0

Subproblem 1
Set the factor '(-36 + -1r)' equal to zero and attempt to solve:

Simplifying
-36 + -1r = 0

Solving
-36 + -1r = 0

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

Add '36' to each side of the equation.
-36 + 36 + -1r = 0 + 36

Combine like terms: -36 + 36 = 0
0 + -1r = 0 + 36
-1r = 0 + 36

Combine like terms: 0 + 36 = 36
-1r = 36

Divide each side by '-1'.
r = -36

Simplifying
r = -36
Subproblem 2
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
Solution
r = {-36, 9}