(2r+1)(8r+5)=0

Solution for (2r+1)(8r+5)=0 equation:

Simplifying
(2r + 1)(8r + 5) = 0

Reorder the terms:
(1 + 2r)(8r + 5) = 0

Reorder the terms:
(1 + 2r)(5 + 8r) = 0

Multiply (1 + 2r) * (5 + 8r)
(1(5 + 8r) + 2r * (5 + 8r)) = 0
((5 * 1 + 8r * 1) + 2r * (5 + 8r)) = 0
((5 + 8r) + 2r * (5 + 8r)) = 0
(5 + 8r + (5 * 2r + 8r * 2r)) = 0
(5 + 8r + (10r + 16r2)) = 0

Combine like terms: 8r + 10r = 18r
(5 + 18r + 16r2) = 0

Solving
5 + 18r + 16r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(5 + 8r)(1 + 2r) = 0

Subproblem 1
Set the factor '(5 + 8r)' equal to zero and attempt to solve:

Simplifying
5 + 8r = 0

Solving
5 + 8r = 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 + 8r = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 8r = 0 + -5
8r = 0 + -5

Combine like terms: 0 + -5 = -5
8r = -5

Divide each side by '8'.
r = -0.625

Simplifying
r = -0.625
Subproblem 2
Set the factor '(1 + 2r)' equal to zero and attempt to solve:

Simplifying
1 + 2r = 0

Solving
1 + 2r = 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 + 2r = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2r = 0 + -1
2r = 0 + -1

Combine like terms: 0 + -1 = -1
2r = -1

Divide each side by '2'.
r = -0.5

Simplifying
r = -0.5
Solution
r = {-0.625, -0.5}