(r-5)(r-9)=

Solution for (r-5)(r-9)= equation:

Simplifying
(r + -5)(r + -9) = 0

Reorder the terms:
(-5 + r)(r + -9) = 0

Reorder the terms:
(-5 + r)(-9 + r) = 0

Multiply (-5 + r) * (-9 + r)
(-5(-9 + r) + r(-9 + r)) = 0
((-9 * -5 + r * -5) + r(-9 + r)) = 0
((45 + -5r) + r(-9 + r)) = 0
(45 + -5r + (-9 * r + r * r)) = 0
(45 + -5r + (-9r + r2)) = 0

Combine like terms: -5r + -9r = -14r
(45 + -14r + r2) = 0

Solving
45 + -14r + r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(5 + -1r)(9 + -1r) = 0

Subproblem 1
Set the factor '(5 + -1r)' equal to zero and attempt to solve:

Simplifying
5 + -1r = 0

Solving
5 + -1r = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1r = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1r = 0 + -5
-1r = 0 + -5

Combine like terms: 0 + -5 = -5
-1r = -5

Divide each side by '-1'.
r = 5

Simplifying
r = 5
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 = {5, 9}