(r-8)(r+1)=0

Solution for (r-8)(r+1)=0 equation:

Simplifying
(r + -8)(r + 1) = 0

Reorder the terms:
(-8 + r)(r + 1) = 0

Reorder the terms:
(-8 + r)(1 + r) = 0

Multiply (-8 + r) * (1 + r)
(-8(1 + r) + r(1 + r)) = 0
((1 * -8 + r * -8) + r(1 + r)) = 0
((-8 + -8r) + r(1 + r)) = 0
(-8 + -8r + (1 * r + r * r)) = 0
(-8 + -8r + (1r + r2)) = 0

Combine like terms: -8r + 1r = -7r
(-8 + -7r + r2) = 0

Solving
-8 + -7r + r2 = 0

Solving for variable 'r'.

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

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

Simplifying
-1 + -1r = 0

Solving
-1 + -1r = 0

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

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

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

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

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

Simplifying
r = -1
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 = {-1, 8}