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

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

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

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

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

Multiply (3 + n) * (1 + 8n)
(3(1 + 8n) + n(1 + 8n)) = 0
((1 * 3 + 8n * 3) + n(1 + 8n)) = 0
((3 + 24n) + n(1 + 8n)) = 0
(3 + 24n + (1 * n + 8n * n)) = 0
(3 + 24n + (1n + 8n2)) = 0

Combine like terms: 24n + 1n = 25n
(3 + 25n + 8n2) = 0

Solving
3 + 25n + 8n2 = 0

Solving for variable 'n'.

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

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

Simplifying
3 + n = 0

Solving
3 + n = 0

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

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

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

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

Simplifying
n = -3
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 = {-3, -0.125}