(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 = 4r
(-45 + 4r + r2) = 0

Solving
-45 + 4r + r2 = 0

Solving for variable 'r'.

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

Subproblem 1
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
Subproblem 2
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
Solution
r = {-9, 5}