(5a+7)(a+5)=32

Solution for (5a+7)(a+5)=32 equation:

Simplifying
(5a + 7)(a + 5) = 32

Reorder the terms:
(7 + 5a)(a + 5) = 32

Reorder the terms:
(7 + 5a)(5 + a) = 32

Multiply (7 + 5a) * (5 + a)
(7(5 + a) + 5a * (5 + a)) = 32
((5 * 7 + a * 7) + 5a * (5 + a)) = 32
((35 + 7a) + 5a * (5 + a)) = 32
(35 + 7a + (5 * 5a + a * 5a)) = 32
(35 + 7a + (25a + 5a2)) = 32

Combine like terms: 7a + 25a = 32a
(35 + 32a + 5a2) = 32

Solving
35 + 32a + 5a2 = 32

Solving for variable 'a'.

Reorder the terms:
35 + -32 + 32a + 5a2 = 32 + -32

Combine like terms: 35 + -32 = 3
3 + 32a + 5a2 = 32 + -32

Combine like terms: 32 + -32 = 0
3 + 32a + 5a2 = 0

Begin completing the square.  Divide all terms by
5 the coefficient of the squared term: 

Divide each side by '5'.
0.6 + 6.4a + a2 = 0

Move the constant term to the right:

Add '-0.6' to each side of the equation.
0.6 + 6.4a + -0.6 + a2 = 0 + -0.6

Reorder the terms:
0.6 + -0.6 + 6.4a + a2 = 0 + -0.6

Combine like terms: 0.6 + -0.6 = 0.0
0.0 + 6.4a + a2 = 0 + -0.6
6.4a + a2 = 0 + -0.6

Combine like terms: 0 + -0.6 = -0.6
6.4a + a2 = -0.6

The a term is 6.4a.  Take half its coefficient (3.2).
Square it (10.24) and add it to both sides.

Add '10.24' to each side of the equation.
6.4a + 10.24 + a2 = -0.6 + 10.24

Reorder the terms:
10.24 + 6.4a + a2 = -0.6 + 10.24

Combine like terms: -0.6 + 10.24 = 9.64
10.24 + 6.4a + a2 = 9.64

Factor a perfect square on the left side:
(a + 3.2)(a + 3.2) = 9.64

Calculate the square root of the right side: 3.104834939

Break this problem into two subproblems by setting 
(a + 3.2) equal to 3.104834939 and -3.104834939.

Subproblem 1
a + 3.2 = 3.104834939

Simplifying
a + 3.2 = 3.104834939

Reorder the terms:
3.2 + a = 3.104834939

Solving
3.2 + a = 3.104834939

Solving for variable 'a'.

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

Add '-3.2' to each side of the equation.
3.2 + -3.2 + a = 3.104834939 + -3.2

Combine like terms: 3.2 + -3.2 = 0.0
0.0 + a = 3.104834939 + -3.2
a = 3.104834939 + -3.2

Combine like terms: 3.104834939 + -3.2 = -0.095165061
a = -0.095165061

Simplifying
a = -0.095165061

Subproblem 2
a + 3.2 = -3.104834939

Simplifying
a + 3.2 = -3.104834939

Reorder the terms:
3.2 + a = -3.104834939

Solving
3.2 + a = -3.104834939

Solving for variable 'a'.

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

Add '-3.2' to each side of the equation.
3.2 + -3.2 + a = -3.104834939 + -3.2

Combine like terms: 3.2 + -3.2 = 0.0
0.0 + a = -3.104834939 + -3.2
a = -3.104834939 + -3.2

Combine like terms: -3.104834939 + -3.2 = -6.304834939
a = -6.304834939

Simplifying
a = -6.304834939

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {-0.095165061, -6.304834939}