(n+1)(8-n+1)=64

Solution for (n+1)(8-n+1)=64 equation:

Simplifying
(n + 1)(8 + -1n + 1) = 64

Reorder the terms:
(1 + n)(8 + -1n + 1) = 64

Reorder the terms:
(1 + n)(8 + 1 + -1n) = 64

Combine like terms: 8 + 1 = 9
(1 + n)(9 + -1n) = 64

Multiply (1 + n) * (9 + -1n)
(1(9 + -1n) + n(9 + -1n)) = 64
((9 * 1 + -1n * 1) + n(9 + -1n)) = 64
((9 + -1n) + n(9 + -1n)) = 64
(9 + -1n + (9 * n + -1n * n)) = 64
(9 + -1n + (9n + -1n2)) = 64

Combine like terms: -1n + 9n = 8n
(9 + 8n + -1n2) = 64

Solving
9 + 8n + -1n2 = 64

Solving for variable 'n'.

Reorder the terms:
9 + -64 + 8n + -1n2 = 64 + -64

Combine like terms: 9 + -64 = -55
-55 + 8n + -1n2 = 64 + -64

Combine like terms: 64 + -64 = 0
-55 + 8n + -1n2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
55 + -8n + n2 = 0

Move the constant term to the right:

Add '-55' to each side of the equation.
55 + -8n + -55 + n2 = 0 + -55

Reorder the terms:
55 + -55 + -8n + n2 = 0 + -55

Combine like terms: 55 + -55 = 0
0 + -8n + n2 = 0 + -55
-8n + n2 = 0 + -55

Combine like terms: 0 + -55 = -55
-8n + n2 = -55

The n term is -8n.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8n + 16 + n2 = -55 + 16

Reorder the terms:
16 + -8n + n2 = -55 + 16

Combine like terms: -55 + 16 = -39
16 + -8n + n2 = -39

Factor a perfect square on the left side:
(n + -4)(n + -4) = -39

Can't calculate square root of the right side.

The solution to this equation could not be determined.