(7n+8)(n+1)=0

Solution for (7n+8)(n+1)=0 equation:

Simplifying
(7n + 8)(n + 1) = 0

Reorder the terms:
(8 + 7n)(n + 1) = 0

Reorder the terms:
(8 + 7n)(1 + n) = 0

Multiply (8 + 7n) * (1 + n)
(8(1 + n) + 7n * (1 + n)) = 0
((1 * 8 + n * 8) + 7n * (1 + n)) = 0
((8 + 8n) + 7n * (1 + n)) = 0
(8 + 8n + (1 * 7n + n * 7n)) = 0
(8 + 8n + (7n + 7n2)) = 0

Combine like terms: 8n + 7n = 15n
(8 + 15n + 7n2) = 0

Solving
8 + 15n + 7n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(8 + 7n)(1 + n) = 0

Subproblem 1
Set the factor '(8 + 7n)' equal to zero and attempt to solve:

Simplifying
8 + 7n = 0

Solving
8 + 7n = 0

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

Add '-8' to each side of the equation.
8 + -8 + 7n = 0 + -8

Combine like terms: 8 + -8 = 0
0 + 7n = 0 + -8
7n = 0 + -8

Combine like terms: 0 + -8 = -8
7n = -8

Divide each side by '7'.
n = -1.142857143

Simplifying
n = -1.142857143
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 = {-1.142857143, -1}