(n+2)(n-5)=49

Solution for (n+2)(n-5)=49 equation:

Simplifying
(n + 2)(n + -5) = 49

Reorder the terms:
(2 + n)(n + -5) = 49

Reorder the terms:
(2 + n)(-5 + n) = 49

Multiply (2 + n) * (-5 + n)
(2(-5 + n) + n(-5 + n)) = 49
((-5 * 2 + n * 2) + n(-5 + n)) = 49
((-10 + 2n) + n(-5 + n)) = 49
(-10 + 2n + (-5 * n + n * n)) = 49
(-10 + 2n + (-5n + n2)) = 49

Combine like terms: 2n + -5n = -3n
(-10 + -3n + n2) = 49

Solving
-10 + -3n + n2 = 49

Solving for variable 'n'.

Reorder the terms:
-10 + -49 + -3n + n2 = 49 + -49

Combine like terms: -10 + -49 = -59
-59 + -3n + n2 = 49 + -49

Combine like terms: 49 + -49 = 0
-59 + -3n + n2 = 0

Begin completing the square.

Move the constant term to the right:

Add '59' to each side of the equation.
-59 + -3n + 59 + n2 = 0 + 59

Reorder the terms:
-59 + 59 + -3n + n2 = 0 + 59

Combine like terms: -59 + 59 = 0
0 + -3n + n2 = 0 + 59
-3n + n2 = 0 + 59

Combine like terms: 0 + 59 = 59
-3n + n2 = 59

The n term is -3n.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3n + 2.25 + n2 = 59 + 2.25

Reorder the terms:
2.25 + -3n + n2 = 59 + 2.25

Combine like terms: 59 + 2.25 = 61.25
2.25 + -3n + n2 = 61.25

Factor a perfect square on the left side:
(n + -1.5)(n + -1.5) = 61.25

Calculate the square root of the right side: 7.826237921

Break this problem into two subproblems by setting 
(n + -1.5) equal to 7.826237921 and -7.826237921.

Subproblem 1
n + -1.5 = 7.826237921

Simplifying
n + -1.5 = 7.826237921

Reorder the terms:
-1.5 + n = 7.826237921

Solving
-1.5 + n = 7.826237921

Solving for variable 'n'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + n = 7.826237921 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + n = 7.826237921 + 1.5
n = 7.826237921 + 1.5

Combine like terms: 7.826237921 + 1.5 = 9.326237921
n = 9.326237921

Simplifying
n = 9.326237921

Subproblem 2
n + -1.5 = -7.826237921

Simplifying
n + -1.5 = -7.826237921

Reorder the terms:
-1.5 + n = -7.826237921

Solving
-1.5 + n = -7.826237921

Solving for variable 'n'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + n = -7.826237921 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + n = -7.826237921 + 1.5
n = -7.826237921 + 1.5

Combine like terms: -7.826237921 + 1.5 = -6.326237921
n = -6.326237921

Simplifying
n = -6.326237921

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {9.326237921, -6.326237921}