(n+1)(n-3)=48

Solution for (n+1)(n-3)=48 equation:

Simplifying
(n + 1)(n + -3) = 48

Reorder the terms:
(1 + n)(n + -3) = 48

Reorder the terms:
(1 + n)(-3 + n) = 48

Multiply (1 + n) * (-3 + n)
(1(-3 + n) + n(-3 + n)) = 48
((-3 * 1 + n * 1) + n(-3 + n)) = 48
((-3 + 1n) + n(-3 + n)) = 48
(-3 + 1n + (-3 * n + n * n)) = 48
(-3 + 1n + (-3n + n2)) = 48

Combine like terms: 1n + -3n = -2n
(-3 + -2n + n2) = 48

Solving
-3 + -2n + n2 = 48

Solving for variable 'n'.

Reorder the terms:
-3 + -48 + -2n + n2 = 48 + -48

Combine like terms: -3 + -48 = -51
-51 + -2n + n2 = 48 + -48

Combine like terms: 48 + -48 = 0
-51 + -2n + n2 = 0

Begin completing the square.

Move the constant term to the right:

Add '51' to each side of the equation.
-51 + -2n + 51 + n2 = 0 + 51

Reorder the terms:
-51 + 51 + -2n + n2 = 0 + 51

Combine like terms: -51 + 51 = 0
0 + -2n + n2 = 0 + 51
-2n + n2 = 0 + 51

Combine like terms: 0 + 51 = 51
-2n + n2 = 51

The n term is -2n.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2n + 1 + n2 = 51 + 1

Reorder the terms:
1 + -2n + n2 = 51 + 1

Combine like terms: 51 + 1 = 52
1 + -2n + n2 = 52

Factor a perfect square on the left side:
(n + -1)(n + -1) = 52

Calculate the square root of the right side: 7.211102551

Break this problem into two subproblems by setting 
(n + -1) equal to 7.211102551 and -7.211102551.

Subproblem 1
n + -1 = 7.211102551

Simplifying
n + -1 = 7.211102551

Reorder the terms:
-1 + n = 7.211102551

Solving
-1 + n = 7.211102551

Solving for variable 'n'.

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 = 7.211102551 + 1

Combine like terms: -1 + 1 = 0
0 + n = 7.211102551 + 1
n = 7.211102551 + 1

Combine like terms: 7.211102551 + 1 = 8.211102551
n = 8.211102551

Simplifying
n = 8.211102551

Subproblem 2
n + -1 = -7.211102551

Simplifying
n + -1 = -7.211102551

Reorder the terms:
-1 + n = -7.211102551

Solving
-1 + n = -7.211102551

Solving for variable 'n'.

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 = -7.211102551 + 1

Combine like terms: -1 + 1 = 0
0 + n = -7.211102551 + 1
n = -7.211102551 + 1

Combine like terms: -7.211102551 + 1 = -6.211102551
n = -6.211102551

Simplifying
n = -6.211102551

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {8.211102551, -6.211102551}