(n+6)(n-1)=130

Solution for (n+6)(n-1)=130 equation:

Simplifying
(n + 6)(n + -1) = 130

Reorder the terms:
(6 + n)(n + -1) = 130

Reorder the terms:
(6 + n)(-1 + n) = 130

Multiply (6 + n) * (-1 + n)
(6(-1 + n) + n(-1 + n)) = 130
((-1 * 6 + n * 6) + n(-1 + n)) = 130
((-6 + 6n) + n(-1 + n)) = 130
(-6 + 6n + (-1 * n + n * n)) = 130
(-6 + 6n + (-1n + n2)) = 130

Combine like terms: 6n + -1n = 5n
(-6 + 5n + n2) = 130

Solving
-6 + 5n + n2 = 130

Solving for variable 'n'.

Reorder the terms:
-6 + -130 + 5n + n2 = 130 + -130

Combine like terms: -6 + -130 = -136
-136 + 5n + n2 = 130 + -130

Combine like terms: 130 + -130 = 0
-136 + 5n + n2 = 0

Begin completing the square.

Move the constant term to the right:

Add '136' to each side of the equation.
-136 + 5n + 136 + n2 = 0 + 136

Reorder the terms:
-136 + 136 + 5n + n2 = 0 + 136

Combine like terms: -136 + 136 = 0
0 + 5n + n2 = 0 + 136
5n + n2 = 0 + 136

Combine like terms: 0 + 136 = 136
5n + n2 = 136

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 = 136 + 6.25

Reorder the terms:
6.25 + 5n + n2 = 136 + 6.25

Combine like terms: 136 + 6.25 = 142.25
6.25 + 5n + n2 = 142.25

Factor a perfect square on the left side:
(n + 2.5)(n + 2.5) = 142.25

Calculate the square root of the right side: 11.926860442

Break this problem into two subproblems by setting 
(n + 2.5) equal to 11.926860442 and -11.926860442.

Subproblem 1
n + 2.5 = 11.926860442

Simplifying
n + 2.5 = 11.926860442

Reorder the terms:
2.5 + n = 11.926860442

Solving
2.5 + n = 11.926860442

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 = 11.926860442 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + n = 11.926860442 + -2.5
n = 11.926860442 + -2.5

Combine like terms: 11.926860442 + -2.5 = 9.426860442
n = 9.426860442

Simplifying
n = 9.426860442

Subproblem 2
n + 2.5 = -11.926860442

Simplifying
n + 2.5 = -11.926860442

Reorder the terms:
2.5 + n = -11.926860442

Solving
2.5 + n = -11.926860442

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 = -11.926860442 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + n = -11.926860442 + -2.5
n = -11.926860442 + -2.5

Combine like terms: -11.926860442 + -2.5 = -14.426860442
n = -14.426860442

Simplifying
n = -14.426860442

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {9.426860442, -14.426860442}