(r-9)(r+16)=0

Solution for (r-9)(r+16)=0 equation:

Simplifying
(r + -9)(r + 16) = 0

Reorder the terms:
(-9 + r)(r + 16) = 0

Reorder the terms:
(-9 + r)(16 + r) = 0

Multiply (-9 + r) * (16 + r)
(-9(16 + r) + r(16 + r)) = 0
((16 * -9 + r * -9) + r(16 + r)) = 0
((-144 + -9r) + r(16 + r)) = 0
(-144 + -9r + (16 * r + r * r)) = 0
(-144 + -9r + (16r + r2)) = 0

Combine like terms: -9r + 16r = 7r
(-144 + 7r + r2) = 0

Solving
-144 + 7r + r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(-16 + -1r)(9 + -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 '(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 = {-16, 9}