30=(n+1)(n+8)

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Solution for 30=(n+1)(n+8) equation: 


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

Reorder the terms:
30 = (1 + n)(n + 8)

Reorder the terms:
30 = (1 + n)(8 + n)

Multiply (1 + n) * (8 + n)
30 = (1(8 + n) + n(8 + n))
30 = ((8 * 1 + n * 1) + n(8 + n))
30 = ((8 + 1n) + n(8 + n))
30 = (8 + 1n + (8 * n + n * n))
30 = (8 + 1n + (8n + n2))

Combine like terms: 1n + 8n = 9n
30 = (8 + 9n + n2)

Solving
30 = 8 + 9n + n2

Solving for variable 'n'.

Combine like terms: 30 + -8 = 22
22 + -9n + -1n2 = 8 + 9n + n2 + -8 + -9n + -1n2

Reorder the terms:
22 + -9n + -1n2 = 8 + -8 + 9n + -9n + n2 + -1n2

Combine like terms: 8 + -8 = 0
22 + -9n + -1n2 = 0 + 9n + -9n + n2 + -1n2
22 + -9n + -1n2 = 9n + -9n + n2 + -1n2

Combine like terms: 9n + -9n = 0
22 + -9n + -1n2 = 0 + n2 + -1n2
22 + -9n + -1n2 = n2 + -1n2

Combine like terms: n2 + -1n2 = 0
22 + -9n + -1n2 = 0

Factor a trinomial.
(2 + -1n)(11 + n) = 0


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

Simplifying
2 + -1n = 0

Solving
2 + -1n = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1n = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1n = 0 + -2
-1n = 0 + -2

Combine like terms: 0 + -2 = -2
-1n = -2

Divide each side by '-1'.
n = 2

Simplifying
n = 2

Subproblem 2
Set the factor '(11 + n)' equal to zero and attempt to solve:

Simplifying
11 + n = 0

Solving
11 + n = 0

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

Add '-11' to each side of the equation.
11 + -11 + n = 0 + -11

Combine like terms: 11 + -11 = 0
0 + n = 0 + -11
n = 0 + -11

Combine like terms: 0 + -11 = -11
n = -11

Simplifying
n = -11
Solution
n = {2, -11}

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