(x+13)(x+5)=-2

Solution for (x+13)(x+5)=-2 equation:

Simplifying
(x + 13)(x + 5) = -2

Reorder the terms:
(13 + x)(x + 5) = -2

Reorder the terms:
(13 + x)(5 + x) = -2

Multiply (13 + x) * (5 + x)
(13(5 + x) + x(5 + x)) = -2
((5 * 13 + x * 13) + x(5 + x)) = -2
((65 + 13x) + x(5 + x)) = -2
(65 + 13x + (5 * x + x * x)) = -2
(65 + 13x + (5x + x2)) = -2

Combine like terms: 13x + 5x = 18x
(65 + 18x + x2) = -2

Solving
65 + 18x + x2 = -2

Solving for variable 'x'.

Reorder the terms:
65 + 2 + 18x + x2 = -2 + 2

Combine like terms: 65 + 2 = 67
67 + 18x + x2 = -2 + 2

Combine like terms: -2 + 2 = 0
67 + 18x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-67' to each side of the equation.
67 + 18x + -67 + x2 = 0 + -67

Reorder the terms:
67 + -67 + 18x + x2 = 0 + -67

Combine like terms: 67 + -67 = 0
0 + 18x + x2 = 0 + -67
18x + x2 = 0 + -67

Combine like terms: 0 + -67 = -67
18x + x2 = -67

The x term is 18x.  Take half its coefficient (9).
Square it (81) and add it to both sides.

Add '81' to each side of the equation.
18x + 81 + x2 = -67 + 81

Reorder the terms:
81 + 18x + x2 = -67 + 81

Combine like terms: -67 + 81 = 14
81 + 18x + x2 = 14

Factor a perfect square on the left side:
(x + 9)(x + 9) = 14

Calculate the square root of the right side: 3.741657387

Break this problem into two subproblems by setting 
(x + 9) equal to 3.741657387 and -3.741657387.

Subproblem 1
x + 9 = 3.741657387

Simplifying
x + 9 = 3.741657387

Reorder the terms:
9 + x = 3.741657387

Solving
9 + x = 3.741657387

Solving for variable 'x'.

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

Add '-9' to each side of the equation.
9 + -9 + x = 3.741657387 + -9

Combine like terms: 9 + -9 = 0
0 + x = 3.741657387 + -9
x = 3.741657387 + -9

Combine like terms: 3.741657387 + -9 = -5.258342613
x = -5.258342613

Simplifying
x = -5.258342613

Subproblem 2
x + 9 = -3.741657387

Simplifying
x + 9 = -3.741657387

Reorder the terms:
9 + x = -3.741657387

Solving
9 + x = -3.741657387

Solving for variable 'x'.

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

Add '-9' to each side of the equation.
9 + -9 + x = -3.741657387 + -9

Combine like terms: 9 + -9 = 0
0 + x = -3.741657387 + -9
x = -3.741657387 + -9

Combine like terms: -3.741657387 + -9 = -12.741657387
x = -12.741657387

Simplifying
x = -12.741657387

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-5.258342613, -12.741657387}