8(5n+1)(3n+4)=0

Solution for 8(5n+1)(3n+4)=0 equation:

Simplifying
8(5n + 1)(3n + 4) = 0

Reorder the terms:
8(1 + 5n)(3n + 4) = 0

Reorder the terms:
8(1 + 5n)(4 + 3n) = 0

Multiply (1 + 5n) * (4 + 3n)
8(1(4 + 3n) + 5n * (4 + 3n)) = 0
8((4 * 1 + 3n * 1) + 5n * (4 + 3n)) = 0
8((4 + 3n) + 5n * (4 + 3n)) = 0
8(4 + 3n + (4 * 5n + 3n * 5n)) = 0
8(4 + 3n + (20n + 15n2)) = 0

Combine like terms: 3n + 20n = 23n
8(4 + 23n + 15n2) = 0
(4 * 8 + 23n * 8 + 15n2 * 8) = 0
(32 + 184n + 120n2) = 0

Solving
32 + 184n + 120n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '8'.
8(4 + 23n + 15n2) = 0

Factor a trinomial.
8((4 + 3n)(1 + 5n)) = 0

Ignore the factor 8.
Subproblem 1
Set the factor '(4 + 3n)' equal to zero and attempt to solve:

Simplifying
4 + 3n = 0

Solving
4 + 3n = 0

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

Add '-4' to each side of the equation.
4 + -4 + 3n = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 3n = 0 + -4
3n = 0 + -4

Combine like terms: 0 + -4 = -4
3n = -4

Divide each side by '3'.
n = -1.333333333

Simplifying
n = -1.333333333
Subproblem 2
Set the factor '(1 + 5n)' equal to zero and attempt to solve:

Simplifying
1 + 5n = 0

Solving
1 + 5n = 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 + 5n = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 5n = 0 + -1
5n = 0 + -1

Combine like terms: 0 + -1 = -1
5n = -1

Divide each side by '5'.
n = -0.2

Simplifying
n = -0.2
Solution
n = {-1.333333333, -0.2}