(8r+1)(r+4)=0

Solution for (8r+1)(r+4)=0 equation:

Simplifying
(8r + 1)(r + 4) = 0

Reorder the terms:
(1 + 8r)(r + 4) = 0

Reorder the terms:
(1 + 8r)(4 + r) = 0

Multiply (1 + 8r) * (4 + r)
(1(4 + r) + 8r * (4 + r)) = 0
((4 * 1 + r * 1) + 8r * (4 + r)) = 0
((4 + 1r) + 8r * (4 + r)) = 0
(4 + 1r + (4 * 8r + r * 8r)) = 0
(4 + 1r + (32r + 8r2)) = 0

Combine like terms: 1r + 32r = 33r
(4 + 33r + 8r2) = 0

Solving
4 + 33r + 8r2 = 0

Solving for variable 'r'.

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

Subproblem 1
Set the factor '(4 + r)' equal to zero and attempt to solve:

Simplifying
4 + r = 0

Solving
4 + r = 0

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

Add '-4' to each side of the equation.
4 + -4 + r = 0 + -4

Combine like terms: 4 + -4 = 0
0 + r = 0 + -4
r = 0 + -4

Combine like terms: 0 + -4 = -4
r = -4

Simplifying
r = -4
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 = {-4, -0.125}