(r-36)(r+16)=0

Solution for (r-36)(r+16)=0 equation:

Simplifying
(r + -36)(r + 16) = 0

Reorder the terms:
(-36 + r)(r + 16) = 0

Reorder the terms:
(-36 + r)(16 + r) = 0

Multiply (-36 + r) * (16 + r)
(-36(16 + r) + r(16 + r)) = 0
((16 * -36 + r * -36) + r(16 + r)) = 0
((-576 + -36r) + r(16 + r)) = 0
(-576 + -36r + (16 * r + r * r)) = 0
(-576 + -36r + (16r + r2)) = 0

Combine like terms: -36r + 16r = -20r
(-576 + -20r + r2) = 0

Solving
-576 + -20r + r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(-16 + -1r)(36 + -1r) = 0

Subproblem 1
Set the factor '(-16 + -1r)' equal to zero and attempt to solve:

Simplifying
-16 + -1r = 0

Solving
-16 + -1r = 0

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

Add '16' to each side of the equation.
-16 + 16 + -1r = 0 + 16

Combine like terms: -16 + 16 = 0
0 + -1r = 0 + 16
-1r = 0 + 16

Combine like terms: 0 + 16 = 16
-1r = 16

Divide each side by '-1'.
r = -16

Simplifying
r = -16
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 = {-16, 36}