(n+1)(n-6)=30

Solution for (n+1)(n-6)=30 equation:

Simplifying
(n + 1)(n + -6) = 30

Reorder the terms:
(1 + n)(n + -6) = 30

Reorder the terms:
(1 + n)(-6 + n) = 30

Multiply (1 + n) * (-6 + n)
(1(-6 + n) + n(-6 + n)) = 30
((-6 * 1 + n * 1) + n(-6 + n)) = 30
((-6 + 1n) + n(-6 + n)) = 30
(-6 + 1n + (-6 * n + n * n)) = 30
(-6 + 1n + (-6n + n2)) = 30

Combine like terms: 1n + -6n = -5n
(-6 + -5n + n2) = 30

Solving
-6 + -5n + n2 = 30

Solving for variable 'n'.

Reorder the terms:
-6 + -30 + -5n + n2 = 30 + -30

Combine like terms: -6 + -30 = -36
-36 + -5n + n2 = 30 + -30

Combine like terms: 30 + -30 = 0
-36 + -5n + n2 = 0

Factor a trinomial.
(-4 + -1n)(9 + -1n) = 0

Subproblem 1
Set the factor '(-4 + -1n)' equal to zero and attempt to solve:

Simplifying
-4 + -1n = 0

Solving
-4 + -1n = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1n = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1n = 0 + 4
-1n = 0 + 4

Combine like terms: 0 + 4 = 4
-1n = 4

Divide each side by '-1'.
n = -4

Simplifying
n = -4
Subproblem 2
Set the factor '(9 + -1n)' equal to zero and attempt to solve:

Simplifying
9 + -1n = 0

Solving
9 + -1n = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1n = 0 + -9

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

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

Divide each side by '-1'.
n = 9

Simplifying
n = 9
Solution
n = {-4, 9}