(n+1)(n-3)=21

Solution for (n+1)(n-3)=21 equation:

Simplifying
(n + 1)(n + -3) = 21

Reorder the terms:
(1 + n)(n + -3) = 21

Reorder the terms:
(1 + n)(-3 + n) = 21

Multiply (1 + n) * (-3 + n)
(1(-3 + n) + n(-3 + n)) = 21
((-3 * 1 + n * 1) + n(-3 + n)) = 21
((-3 + 1n) + n(-3 + n)) = 21
(-3 + 1n + (-3 * n + n * n)) = 21
(-3 + 1n + (-3n + n2)) = 21

Combine like terms: 1n + -3n = -2n
(-3 + -2n + n2) = 21

Solving
-3 + -2n + n2 = 21

Solving for variable 'n'.

Reorder the terms:
-3 + -21 + -2n + n2 = 21 + -21

Combine like terms: -3 + -21 = -24
-24 + -2n + n2 = 21 + -21

Combine like terms: 21 + -21 = 0
-24 + -2n + n2 = 0

Factor a trinomial.
(-4 + -1n)(6 + -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 '(6 + -1n)' equal to zero and attempt to solve:

Simplifying
6 + -1n = 0

Solving
6 + -1n = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1n = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1n = 0 + -6
-1n = 0 + -6

Combine like terms: 0 + -6 = -6
-1n = -6

Divide each side by '-1'.
n = 6

Simplifying
n = 6
Solution
n = {-4, 6}