=(n+7)(n+1)

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

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

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

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

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

Combine like terms: 7n + 1n = 8n
0 = (7 + 8n + n2)

Solving
0 = 7 + 8n + n2

Solving for variable 'n'.

Combine like terms: 0 + -7 = -7
-7 + -8n + -1n2 = 7 + 8n + n2 + -7 + -8n + -1n2

Reorder the terms:
-7 + -8n + -1n2 = 7 + -7 + 8n + -8n + n2 + -1n2

Combine like terms: 7 + -7 = 0
-7 + -8n + -1n2 = 0 + 8n + -8n + n2 + -1n2
-7 + -8n + -1n2 = 8n + -8n + n2 + -1n2

Combine like terms: 8n + -8n = 0
-7 + -8n + -1n2 = 0 + n2 + -1n2
-7 + -8n + -1n2 = n2 + -1n2

Combine like terms: n2 + -1n2 = 0
-7 + -8n + -1n2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(7 + 8n + n2) = 0

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

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

Simplifying
7 + n = 0

Solving
7 + n = 0

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

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

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

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

Simplifying
n = -7
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 = {-7, -1}