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

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

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

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

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

Multiply (8 + r) * (1 + 8r)
(8(1 + 8r) + r(1 + 8r)) = 0
((1 * 8 + 8r * 8) + r(1 + 8r)) = 0
((8 + 64r) + r(1 + 8r)) = 0
(8 + 64r + (1 * r + 8r * r)) = 0
(8 + 64r + (1r + 8r2)) = 0

Combine like terms: 64r + 1r = 65r
(8 + 65r + 8r2) = 0

Solving
8 + 65r + 8r2 = 0

Solving for variable 'r'.

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

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

Simplifying
8 + r = 0

Solving
8 + r = 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 + r = 0 + -8

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

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

Simplifying
r = -8
Subproblem 2
Set the factor '(1 + 8r)' equal to zero and attempt to solve:

Simplifying
1 + 8r = 0

Solving
1 + 8r = 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 + 8r = 0 + -1

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

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

Divide each side by '8'.
r = -0.125

Simplifying
r = -0.125
Solution
r = {-8, -0.125}