(n-8)(n+1)=35

Solution for (n-8)(n+1)=35 equation:

Simplifying
(n + -8)(n + 1) = 35

Reorder the terms:
(-8 + n)(n + 1) = 35

Reorder the terms:
(-8 + n)(1 + n) = 35

Multiply (-8 + n) * (1 + n)
(-8(1 + n) + n(1 + n)) = 35
((1 * -8 + n * -8) + n(1 + n)) = 35
((-8 + -8n) + n(1 + n)) = 35
(-8 + -8n + (1 * n + n * n)) = 35
(-8 + -8n + (1n + n2)) = 35

Combine like terms: -8n + 1n = -7n
(-8 + -7n + n2) = 35

Solving
-8 + -7n + n2 = 35

Solving for variable 'n'.

Reorder the terms:
-8 + -35 + -7n + n2 = 35 + -35

Combine like terms: -8 + -35 = -43
-43 + -7n + n2 = 35 + -35

Combine like terms: 35 + -35 = 0
-43 + -7n + n2 = 0

Begin completing the square.

Move the constant term to the right:

Add '43' to each side of the equation.
-43 + -7n + 43 + n2 = 0 + 43

Reorder the terms:
-43 + 43 + -7n + n2 = 0 + 43

Combine like terms: -43 + 43 = 0
0 + -7n + n2 = 0 + 43
-7n + n2 = 0 + 43

Combine like terms: 0 + 43 = 43
-7n + n2 = 43

The n term is -7n.  Take half its coefficient (-3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
-7n + 12.25 + n2 = 43 + 12.25

Reorder the terms:
12.25 + -7n + n2 = 43 + 12.25

Combine like terms: 43 + 12.25 = 55.25
12.25 + -7n + n2 = 55.25

Factor a perfect square on the left side:
(n + -3.5)(n + -3.5) = 55.25

Calculate the square root of the right side: 7.433034374

Break this problem into two subproblems by setting 
(n + -3.5) equal to 7.433034374 and -7.433034374.

Subproblem 1
n + -3.5 = 7.433034374

Simplifying
n + -3.5 = 7.433034374

Reorder the terms:
-3.5 + n = 7.433034374

Solving
-3.5 + n = 7.433034374

Solving for variable 'n'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + n = 7.433034374 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + n = 7.433034374 + 3.5
n = 7.433034374 + 3.5

Combine like terms: 7.433034374 + 3.5 = 10.933034374
n = 10.933034374

Simplifying
n = 10.933034374

Subproblem 2
n + -3.5 = -7.433034374

Simplifying
n + -3.5 = -7.433034374

Reorder the terms:
-3.5 + n = -7.433034374

Solving
-3.5 + n = -7.433034374

Solving for variable 'n'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + n = -7.433034374 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + n = -7.433034374 + 3.5
n = -7.433034374 + 3.5

Combine like terms: -7.433034374 + 3.5 = -3.933034374
n = -3.933034374

Simplifying
n = -3.933034374

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {10.933034374, -3.933034374}