(r-5)(r+8)=0

Solution for (r-5)(r+8)=0 equation:

Simplifying
(r + -5)(r + 8) = 0

Reorder the terms:
(-5 + r)(r + 8) = 0

Reorder the terms:
(-5 + r)(8 + r) = 0

Multiply (-5 + r) * (8 + r)
(-5(8 + r) + r(8 + r)) = 0
((8 * -5 + r * -5) + r(8 + r)) = 0
((-40 + -5r) + r(8 + r)) = 0
(-40 + -5r + (8 * r + r * r)) = 0
(-40 + -5r + (8r + r2)) = 0

Combine like terms: -5r + 8r = 3r
(-40 + 3r + r2) = 0

Solving
-40 + 3r + r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(-8 + -1r)(5 + -1r) = 0

Subproblem 1
Set the factor '(-8 + -1r)' equal to zero and attempt to solve:

Simplifying
-8 + -1r = 0

Solving
-8 + -1r = 0

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

Add '8' to each side of the equation.
-8 + 8 + -1r = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1r = 0 + 8
-1r = 0 + 8

Combine like terms: 0 + 8 = 8
-1r = 8

Divide each side by '-1'.
r = -8

Simplifying
r = -8
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 = {-8, 5}