8(n+1)(2n+3)=0

Solution for 8(n+1)(2n+3)=0 equation:

Simplifying
8(n + 1)(2n + 3) = 0

Reorder the terms:
8(1 + n)(2n + 3) = 0

Reorder the terms:
8(1 + n)(3 + 2n) = 0

Multiply (1 + n) * (3 + 2n)
8(1(3 + 2n) + n(3 + 2n)) = 0
8((3 * 1 + 2n * 1) + n(3 + 2n)) = 0
8((3 + 2n) + n(3 + 2n)) = 0
8(3 + 2n + (3 * n + 2n * n)) = 0
8(3 + 2n + (3n + 2n2)) = 0

Combine like terms: 2n + 3n = 5n
8(3 + 5n + 2n2) = 0
(3 * 8 + 5n * 8 + 2n2 * 8) = 0
(24 + 40n + 16n2) = 0

Solving
24 + 40n + 16n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '8'.
8(3 + 5n + 2n2) = 0

Factor a trinomial.
8((3 + 2n)(1 + n)) = 0

Ignore the factor 8.
Subproblem 1
Set the factor '(3 + 2n)' equal to zero and attempt to solve:

Simplifying
3 + 2n = 0

Solving
3 + 2n = 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 + 2n = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2n = 0 + -3
2n = 0 + -3

Combine like terms: 0 + -3 = -3
2n = -3

Divide each side by '2'.
n = -1.5

Simplifying
n = -1.5
Subproblem 2
Set the factor '(1 + n)' equal to zero and attempt to solve:

Simplifying
1 + n = 0

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

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

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

Simplifying
n = -1
Solution
n = {-1.5, -1}