2(a-4)=4a(2a+8)

Solution for 2(a-4)=4a(2a+8) equation:

Simplifying
2(a + -4) = 4a(2a + 8)

Reorder the terms:
2(-4 + a) = 4a(2a + 8)
(-4 * 2 + a * 2) = 4a(2a + 8)
(-8 + 2a) = 4a(2a + 8)

Reorder the terms:
-8 + 2a = 4a(8 + 2a)
-8 + 2a = (8 * 4a + 2a * 4a)
-8 + 2a = (32a + 8a2)

Solving
-8 + 2a = 32a + 8a2

Solving for variable 'a'.

Combine like terms: 2a + -32a = -30a
-8 + -30a + -8a2 = 32a + 8a2 + -32a + -8a2

Reorder the terms:
-8 + -30a + -8a2 = 32a + -32a + 8a2 + -8a2

Combine like terms: 32a + -32a = 0
-8 + -30a + -8a2 = 0 + 8a2 + -8a2
-8 + -30a + -8a2 = 8a2 + -8a2

Combine like terms: 8a2 + -8a2 = 0
-8 + -30a + -8a2 = 0

Factor out the Greatest Common Factor (GCF), '-2'.
-2(4 + 15a + 4a2) = 0

Ignore the factor -2.
Subproblem 1
Set the factor '(4 + 15a + 4a2)' equal to zero and attempt to solve:

Simplifying
4 + 15a + 4a2 = 0

Solving
4 + 15a + 4a2 = 0

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

Divide each side by '4'.
1 + 3.75a + a2 = 0

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + 3.75a + -1 + a2 = 0 + -1

Reorder the terms:
1 + -1 + 3.75a + a2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 3.75a + a2 = 0 + -1
3.75a + a2 = 0 + -1

Combine like terms: 0 + -1 = -1
3.75a + a2 = -1

The a term is 3.75a.  Take half its coefficient (1.875).
Square it (3.515625) and add it to both sides.

Add '3.515625' to each side of the equation.
3.75a + 3.515625 + a2 = -1 + 3.515625

Reorder the terms:
3.515625 + 3.75a + a2 = -1 + 3.515625

Combine like terms: -1 + 3.515625 = 2.515625
3.515625 + 3.75a + a2 = 2.515625

Factor a perfect square on the left side:
(a + 1.875)(a + 1.875) = 2.515625

Calculate the square root of the right side: 1.586072193

Break this problem into two subproblems by setting 
(a + 1.875) equal to 1.586072193 and -1.586072193.

Subproblem 1
a + 1.875 = 1.586072193

Simplifying
a + 1.875 = 1.586072193

Reorder the terms:
1.875 + a = 1.586072193

Solving
1.875 + a = 1.586072193

Solving for variable 'a'.

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

Add '-1.875' to each side of the equation.
1.875 + -1.875 + a = 1.586072193 + -1.875

Combine like terms: 1.875 + -1.875 = 0.000
0.000 + a = 1.586072193 + -1.875
a = 1.586072193 + -1.875

Combine like terms: 1.586072193 + -1.875 = -0.288927807
a = -0.288927807

Simplifying
a = -0.288927807

Subproblem 2
a + 1.875 = -1.586072193

Simplifying
a + 1.875 = -1.586072193

Reorder the terms:
1.875 + a = -1.586072193

Solving
1.875 + a = -1.586072193

Solving for variable 'a'.

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

Add '-1.875' to each side of the equation.
1.875 + -1.875 + a = -1.586072193 + -1.875

Combine like terms: 1.875 + -1.875 = 0.000
0.000 + a = -1.586072193 + -1.875
a = -1.586072193 + -1.875

Combine like terms: -1.586072193 + -1.875 = -3.461072193
a = -3.461072193

Simplifying
a = -3.461072193

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {-0.288927807, -3.461072193}
Solution
a = {-0.288927807, -3.461072193}