(a+5)(a+7)=2

Solution for (a+5)(a+7)=2 equation:

Simplifying
(a + 5)(a + 7) = 2

Reorder the terms:
(5 + a)(a + 7) = 2

Reorder the terms:
(5 + a)(7 + a) = 2

Multiply (5 + a) * (7 + a)
(5(7 + a) + a(7 + a)) = 2
((7 * 5 + a * 5) + a(7 + a)) = 2
((35 + 5a) + a(7 + a)) = 2
(35 + 5a + (7 * a + a * a)) = 2
(35 + 5a + (7a + a2)) = 2

Combine like terms: 5a + 7a = 12a
(35 + 12a + a2) = 2

Solving
35 + 12a + a2 = 2

Solving for variable 'a'.

Reorder the terms:
35 + -2 + 12a + a2 = 2 + -2

Combine like terms: 35 + -2 = 33
33 + 12a + a2 = 2 + -2

Combine like terms: 2 + -2 = 0
33 + 12a + a2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-33' to each side of the equation.
33 + 12a + -33 + a2 = 0 + -33

Reorder the terms:
33 + -33 + 12a + a2 = 0 + -33

Combine like terms: 33 + -33 = 0
0 + 12a + a2 = 0 + -33
12a + a2 = 0 + -33

Combine like terms: 0 + -33 = -33
12a + a2 = -33

The a term is 12a.  Take half its coefficient (6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
12a + 36 + a2 = -33 + 36

Reorder the terms:
36 + 12a + a2 = -33 + 36

Combine like terms: -33 + 36 = 3
36 + 12a + a2 = 3

Factor a perfect square on the left side:
(a + 6)(a + 6) = 3

Calculate the square root of the right side: 1.732050808

Break this problem into two subproblems by setting 
(a + 6) equal to 1.732050808 and -1.732050808.

Subproblem 1
a + 6 = 1.732050808

Simplifying
a + 6 = 1.732050808

Reorder the terms:
6 + a = 1.732050808

Solving
6 + a = 1.732050808

Solving for variable 'a'.

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

Add '-6' to each side of the equation.
6 + -6 + a = 1.732050808 + -6

Combine like terms: 6 + -6 = 0
0 + a = 1.732050808 + -6
a = 1.732050808 + -6

Combine like terms: 1.732050808 + -6 = -4.267949192
a = -4.267949192

Simplifying
a = -4.267949192

Subproblem 2
a + 6 = -1.732050808

Simplifying
a + 6 = -1.732050808

Reorder the terms:
6 + a = -1.732050808

Solving
6 + a = -1.732050808

Solving for variable 'a'.

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

Add '-6' to each side of the equation.
6 + -6 + a = -1.732050808 + -6

Combine like terms: 6 + -6 = 0
0 + a = -1.732050808 + -6
a = -1.732050808 + -6

Combine like terms: -1.732050808 + -6 = -7.732050808
a = -7.732050808

Simplifying
a = -7.732050808

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {-4.267949192, -7.732050808}