(n+1)(n+4)=36

Solution for (n+1)(n+4)=36 equation:

Simplifying
(n + 1)(n + 4) = 36

Reorder the terms:
(1 + n)(n + 4) = 36

Reorder the terms:
(1 + n)(4 + n) = 36

Multiply (1 + n) * (4 + n)
(1(4 + n) + n(4 + n)) = 36
((4 * 1 + n * 1) + n(4 + n)) = 36
((4 + 1n) + n(4 + n)) = 36
(4 + 1n + (4 * n + n * n)) = 36
(4 + 1n + (4n + n2)) = 36

Combine like terms: 1n + 4n = 5n
(4 + 5n + n2) = 36

Solving
4 + 5n + n2 = 36

Solving for variable 'n'.

Reorder the terms:
4 + -36 + 5n + n2 = 36 + -36

Combine like terms: 4 + -36 = -32
-32 + 5n + n2 = 36 + -36

Combine like terms: 36 + -36 = 0
-32 + 5n + n2 = 0

Begin completing the square.

Move the constant term to the right:

Add '32' to each side of the equation.
-32 + 5n + 32 + n2 = 0 + 32

Reorder the terms:
-32 + 32 + 5n + n2 = 0 + 32

Combine like terms: -32 + 32 = 0
0 + 5n + n2 = 0 + 32
5n + n2 = 0 + 32

Combine like terms: 0 + 32 = 32
5n + n2 = 32

The n term is 5n.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5n + 6.25 + n2 = 32 + 6.25

Reorder the terms:
6.25 + 5n + n2 = 32 + 6.25

Combine like terms: 32 + 6.25 = 38.25
6.25 + 5n + n2 = 38.25

Factor a perfect square on the left side:
(n + 2.5)(n + 2.5) = 38.25

Calculate the square root of the right side: 6.184658438

Break this problem into two subproblems by setting 
(n + 2.5) equal to 6.184658438 and -6.184658438.

Subproblem 1
n + 2.5 = 6.184658438

Simplifying
n + 2.5 = 6.184658438

Reorder the terms:
2.5 + n = 6.184658438

Solving
2.5 + n = 6.184658438

Solving for variable 'n'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + n = 6.184658438 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + n = 6.184658438 + -2.5
n = 6.184658438 + -2.5

Combine like terms: 6.184658438 + -2.5 = 3.684658438
n = 3.684658438

Simplifying
n = 3.684658438

Subproblem 2
n + 2.5 = -6.184658438

Simplifying
n + 2.5 = -6.184658438

Reorder the terms:
2.5 + n = -6.184658438

Solving
2.5 + n = -6.184658438

Solving for variable 'n'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + n = -6.184658438 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + n = -6.184658438 + -2.5
n = -6.184658438 + -2.5

Combine like terms: -6.184658438 + -2.5 = -8.684658438
n = -8.684658438

Simplifying
n = -8.684658438

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {3.684658438, -8.684658438}