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

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

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

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

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

Multiply (6 + 5n) * (1 + 8n)
(6(1 + 8n) + 5n * (1 + 8n)) = 0
((1 * 6 + 8n * 6) + 5n * (1 + 8n)) = 0
((6 + 48n) + 5n * (1 + 8n)) = 0
(6 + 48n + (1 * 5n + 8n * 5n)) = 0
(6 + 48n + (5n + 40n2)) = 0

Combine like terms: 48n + 5n = 53n
(6 + 53n + 40n2) = 0

Solving
6 + 53n + 40n2 = 0

Solving for variable 'n'.

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

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

Simplifying
6 + 5n = 0

Solving
6 + 5n = 0

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

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

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

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

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

Simplifying
n = -1.2
Subproblem 2
Set the factor '(1 + 8n)' equal to zero and attempt to solve:

Simplifying
1 + 8n = 0

Solving
1 + 8n = 0

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

Add '-1' to each side of the equation.
1 + -1 + 8n = 0 + -1

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

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

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

Simplifying
n = -0.125
Solution
n = {-1.2, -0.125}