(8r+1)(5r+6)=0

Solution for (8r+1)(5r+6)=0 equation:

Simplifying
(8r + 1)(5r + 6) = 0

Reorder the terms:
(1 + 8r)(5r + 6) = 0

Reorder the terms:
(1 + 8r)(6 + 5r) = 0

Multiply (1 + 8r) * (6 + 5r)
(1(6 + 5r) + 8r * (6 + 5r)) = 0
((6 * 1 + 5r * 1) + 8r * (6 + 5r)) = 0
((6 + 5r) + 8r * (6 + 5r)) = 0
(6 + 5r + (6 * 8r + 5r * 8r)) = 0
(6 + 5r + (48r + 40r2)) = 0

Combine like terms: 5r + 48r = 53r
(6 + 53r + 40r2) = 0

Solving
6 + 53r + 40r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(6 + 5r)(1 + 8r) = 0

Subproblem 1
Set the factor '(6 + 5r)' equal to zero and attempt to solve:

Simplifying
6 + 5r = 0

Solving
6 + 5r = 0

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

Add '-6' to each side of the equation.
6 + -6 + 5r = 0 + -6

Combine like terms: 6 + -6 = 0
0 + 5r = 0 + -6
5r = 0 + -6

Combine like terms: 0 + -6 = -6
5r = -6

Divide each side by '5'.
r = -1.2

Simplifying
r = -1.2
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 = {-1.2, -0.125}