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

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

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

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

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

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

Combine like terms: 1n + 8n = 9n
0 = (8 + 9n + n2)

Solving
0 = 8 + 9n + n2

Solving for variable 'n'.

Combine like terms: 0 + -8 = -8
-8 + -9n + -1n2 = 8 + 9n + n2 + -8 + -9n + -1n2

Reorder the terms:
-8 + -9n + -1n2 = 8 + -8 + 9n + -9n + n2 + -1n2

Combine like terms: 8 + -8 = 0
-8 + -9n + -1n2 = 0 + 9n + -9n + n2 + -1n2
-8 + -9n + -1n2 = 9n + -9n + n2 + -1n2

Combine like terms: 9n + -9n = 0
-8 + -9n + -1n2 = 0 + n2 + -1n2
-8 + -9n + -1n2 = n2 + -1n2

Combine like terms: n2 + -1n2 = 0
-8 + -9n + -1n2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(8 + 9n + n2) = 0

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

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

Simplifying
8 + n = 0

Solving
8 + n = 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 + n = 0 + -8

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

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

Simplifying
n = -8
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 = {-8, -1}