(n+6)(n-1)=85

Solution for (n+6)(n-1)=85 equation:

Simplifying
(n + 6)(n + -1) = 85

Reorder the terms:
(6 + n)(n + -1) = 85

Reorder the terms:
(6 + n)(-1 + n) = 85

Multiply (6 + n) * (-1 + n)
(6(-1 + n) + n(-1 + n)) = 85
((-1 * 6 + n * 6) + n(-1 + n)) = 85
((-6 + 6n) + n(-1 + n)) = 85
(-6 + 6n + (-1 * n + n * n)) = 85
(-6 + 6n + (-1n + n2)) = 85

Combine like terms: 6n + -1n = 5n
(-6 + 5n + n2) = 85

Solving
-6 + 5n + n2 = 85

Solving for variable 'n'.

Reorder the terms:
-6 + -85 + 5n + n2 = 85 + -85

Combine like terms: -6 + -85 = -91
-91 + 5n + n2 = 85 + -85

Combine like terms: 85 + -85 = 0
-91 + 5n + n2 = 0

Begin completing the square.

Move the constant term to the right:

Add '91' to each side of the equation.
-91 + 5n + 91 + n2 = 0 + 91

Reorder the terms:
-91 + 91 + 5n + n2 = 0 + 91

Combine like terms: -91 + 91 = 0
0 + 5n + n2 = 0 + 91
5n + n2 = 0 + 91

Combine like terms: 0 + 91 = 91
5n + n2 = 91

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 = 91 + 6.25

Reorder the terms:
6.25 + 5n + n2 = 91 + 6.25

Combine like terms: 91 + 6.25 = 97.25
6.25 + 5n + n2 = 97.25

Factor a perfect square on the left side:
(n + 2.5)(n + 2.5) = 97.25

Calculate the square root of the right side: 9.861541462

Break this problem into two subproblems by setting 
(n + 2.5) equal to 9.861541462 and -9.861541462.

Subproblem 1
n + 2.5 = 9.861541462

Simplifying
n + 2.5 = 9.861541462

Reorder the terms:
2.5 + n = 9.861541462

Solving
2.5 + n = 9.861541462

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 = 9.861541462 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + n = 9.861541462 + -2.5
n = 9.861541462 + -2.5

Combine like terms: 9.861541462 + -2.5 = 7.361541462
n = 7.361541462

Simplifying
n = 7.361541462

Subproblem 2
n + 2.5 = -9.861541462

Simplifying
n + 2.5 = -9.861541462

Reorder the terms:
2.5 + n = -9.861541462

Solving
2.5 + n = -9.861541462

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 = -9.861541462 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + n = -9.861541462 + -2.5
n = -9.861541462 + -2.5

Combine like terms: -9.861541462 + -2.5 = -12.361541462
n = -12.361541462

Simplifying
n = -12.361541462

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {7.361541462, -12.361541462}