(n+2)(n-3)=65

Solution for (n+2)(n-3)=65 equation:

Simplifying
(n + 2)(n + -3) = 65

Reorder the terms:
(2 + n)(n + -3) = 65

Reorder the terms:
(2 + n)(-3 + n) = 65

Multiply (2 + n) * (-3 + n)
(2(-3 + n) + n(-3 + n)) = 65
((-3 * 2 + n * 2) + n(-3 + n)) = 65
((-6 + 2n) + n(-3 + n)) = 65
(-6 + 2n + (-3 * n + n * n)) = 65
(-6 + 2n + (-3n + n2)) = 65

Combine like terms: 2n + -3n = -1n
(-6 + -1n + n2) = 65

Solving
-6 + -1n + n2 = 65

Solving for variable 'n'.

Reorder the terms:
-6 + -65 + -1n + n2 = 65 + -65

Combine like terms: -6 + -65 = -71
-71 + -1n + n2 = 65 + -65

Combine like terms: 65 + -65 = 0
-71 + -1n + n2 = 0

Begin completing the square.

Move the constant term to the right:

Add '71' to each side of the equation.
-71 + -1n + 71 + n2 = 0 + 71

Reorder the terms:
-71 + 71 + -1n + n2 = 0 + 71

Combine like terms: -71 + 71 = 0
0 + -1n + n2 = 0 + 71
-1n + n2 = 0 + 71

Combine like terms: 0 + 71 = 71
-1n + n2 = 71

The n term is -1n.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1n + 0.25 + n2 = 71 + 0.25

Reorder the terms:
0.25 + -1n + n2 = 71 + 0.25

Combine like terms: 71 + 0.25 = 71.25
0.25 + -1n + n2 = 71.25

Factor a perfect square on the left side:
(n + -0.5)(n + -0.5) = 71.25

Calculate the square root of the right side: 8.440971508

Break this problem into two subproblems by setting 
(n + -0.5) equal to 8.440971508 and -8.440971508.

Subproblem 1
n + -0.5 = 8.440971508

Simplifying
n + -0.5 = 8.440971508

Reorder the terms:
-0.5 + n = 8.440971508

Solving
-0.5 + n = 8.440971508

Solving for variable 'n'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + n = 8.440971508 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + n = 8.440971508 + 0.5
n = 8.440971508 + 0.5

Combine like terms: 8.440971508 + 0.5 = 8.940971508
n = 8.940971508

Simplifying
n = 8.940971508

Subproblem 2
n + -0.5 = -8.440971508

Simplifying
n + -0.5 = -8.440971508

Reorder the terms:
-0.5 + n = -8.440971508

Solving
-0.5 + n = -8.440971508

Solving for variable 'n'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + n = -8.440971508 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + n = -8.440971508 + 0.5
n = -8.440971508 + 0.5

Combine like terms: -8.440971508 + 0.5 = -7.940971508
n = -7.940971508

Simplifying
n = -7.940971508

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {8.940971508, -7.940971508}