(r-36)(r+81)=0

Solution for (r-36)(r+81)=0 equation:

Simplifying
(r + -36)(r + 81) = 0

Reorder the terms:
(-36 + r)(r + 81) = 0

Reorder the terms:
(-36 + r)(81 + r) = 0

Multiply (-36 + r) * (81 + r)
(-36(81 + r) + r(81 + r)) = 0
((81 * -36 + r * -36) + r(81 + r)) = 0
((-2916 + -36r) + r(81 + r)) = 0
(-2916 + -36r + (81 * r + r * r)) = 0
(-2916 + -36r + (81r + r2)) = 0

Combine like terms: -36r + 81r = 45r
(-2916 + 45r + r2) = 0

Solving
-2916 + 45r + r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(-81 + -1r)(36 + -1r) = 0

Subproblem 1
Set the factor '(-81 + -1r)' equal to zero and attempt to solve:

Simplifying
-81 + -1r = 0

Solving
-81 + -1r = 0

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

Add '81' to each side of the equation.
-81 + 81 + -1r = 0 + 81

Combine like terms: -81 + 81 = 0
0 + -1r = 0 + 81
-1r = 0 + 81

Combine like terms: 0 + 81 = 81
-1r = 81

Divide each side by '-1'.
r = -81

Simplifying
r = -81
Subproblem 2
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
Solution
r = {-81, 36}