(r-9)(r-4)=0

Solution for (r-9)(r-4)=0 equation:

Simplifying
(r + -9)(r + -4) = 0

Reorder the terms:
(-9 + r)(r + -4) = 0

Reorder the terms:
(-9 + r)(-4 + r) = 0

Multiply (-9 + r) * (-4 + r)
(-9(-4 + r) + r(-4 + r)) = 0
((-4 * -9 + r * -9) + r(-4 + r)) = 0
((36 + -9r) + r(-4 + r)) = 0
(36 + -9r + (-4 * r + r * r)) = 0
(36 + -9r + (-4r + r2)) = 0

Combine like terms: -9r + -4r = -13r
(36 + -13r + r2) = 0

Solving
36 + -13r + r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(4 + -1r)(9 + -1r) = 0

Subproblem 1
Set the factor '(4 + -1r)' equal to zero and attempt to solve:

Simplifying
4 + -1r = 0

Solving
4 + -1r = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1r = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1r = 0 + -4
-1r = 0 + -4

Combine like terms: 0 + -4 = -4
-1r = -4

Divide each side by '-1'.
r = 4

Simplifying
r = 4
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 = {4, 9}