4(a-5)=8a(4a+20)

Solution for 4(a-5)=8a(4a+20) equation:

Simplifying
4(a + -5) = 8a(4a + 20)

Reorder the terms:
4(-5 + a) = 8a(4a + 20)
(-5 * 4 + a * 4) = 8a(4a + 20)
(-20 + 4a) = 8a(4a + 20)

Reorder the terms:
-20 + 4a = 8a(20 + 4a)
-20 + 4a = (20 * 8a + 4a * 8a)
-20 + 4a = (160a + 32a2)

Solving
-20 + 4a = 160a + 32a2

Solving for variable 'a'.

Combine like terms: 4a + -160a = -156a
-20 + -156a + -32a2 = 160a + 32a2 + -160a + -32a2

Reorder the terms:
-20 + -156a + -32a2 = 160a + -160a + 32a2 + -32a2

Combine like terms: 160a + -160a = 0
-20 + -156a + -32a2 = 0 + 32a2 + -32a2
-20 + -156a + -32a2 = 32a2 + -32a2

Combine like terms: 32a2 + -32a2 = 0
-20 + -156a + -32a2 = 0

Factor out the Greatest Common Factor (GCF), '-4'.
-4(5 + 39a + 8a2) = 0

Ignore the factor -4.
Subproblem 1
Set the factor '(5 + 39a + 8a2)' equal to zero and attempt to solve:

Simplifying
5 + 39a + 8a2 = 0

Solving
5 + 39a + 8a2 = 0

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

Divide each side by '8'.
0.625 + 4.875a + a2 = 0

Move the constant term to the right:

Add '-0.625' to each side of the equation.
0.625 + 4.875a + -0.625 + a2 = 0 + -0.625

Reorder the terms:
0.625 + -0.625 + 4.875a + a2 = 0 + -0.625

Combine like terms: 0.625 + -0.625 = 0.000
0.000 + 4.875a + a2 = 0 + -0.625
4.875a + a2 = 0 + -0.625

Combine like terms: 0 + -0.625 = -0.625
4.875a + a2 = -0.625

The a term is 4.875a.  Take half its coefficient (2.4375).
Square it (5.94140625) and add it to both sides.

Add '5.94140625' to each side of the equation.
4.875a + 5.94140625 + a2 = -0.625 + 5.94140625

Reorder the terms:
5.94140625 + 4.875a + a2 = -0.625 + 5.94140625

Combine like terms: -0.625 + 5.94140625 = 5.31640625
5.94140625 + 4.875a + a2 = 5.31640625

Factor a perfect square on the left side:
(a + 2.4375)(a + 2.4375) = 5.31640625

Calculate the square root of the right side: 2.305733343

Break this problem into two subproblems by setting 
(a + 2.4375) equal to 2.305733343 and -2.305733343.

Subproblem 1
a + 2.4375 = 2.305733343

Simplifying
a + 2.4375 = 2.305733343

Reorder the terms:
2.4375 + a = 2.305733343

Solving
2.4375 + a = 2.305733343

Solving for variable 'a'.

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

Add '-2.4375' to each side of the equation.
2.4375 + -2.4375 + a = 2.305733343 + -2.4375

Combine like terms: 2.4375 + -2.4375 = 0.0000
0.0000 + a = 2.305733343 + -2.4375
a = 2.305733343 + -2.4375

Combine like terms: 2.305733343 + -2.4375 = -0.131766657
a = -0.131766657

Simplifying
a = -0.131766657

Subproblem 2
a + 2.4375 = -2.305733343

Simplifying
a + 2.4375 = -2.305733343

Reorder the terms:
2.4375 + a = -2.305733343

Solving
2.4375 + a = -2.305733343

Solving for variable 'a'.

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

Add '-2.4375' to each side of the equation.
2.4375 + -2.4375 + a = -2.305733343 + -2.4375

Combine like terms: 2.4375 + -2.4375 = 0.0000
0.0000 + a = -2.305733343 + -2.4375
a = -2.305733343 + -2.4375

Combine like terms: -2.305733343 + -2.4375 = -4.743233343
a = -4.743233343

Simplifying
a = -4.743233343

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {-0.131766657, -4.743233343}
Solution
a = {-0.131766657, -4.743233343}