(r-8)(r+5)=

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

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

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

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

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

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

Solving
-40 + -3r + r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(-5 + -1r)(8 + -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 '(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
Solution
r = {-5, 8}