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

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

Simplifying
2(a + -4) = 4a + -1a(2a + 4)

Reorder the terms:
2(-4 + a) = 4a + -1a(2a + 4)
(-4 * 2 + a * 2) = 4a + -1a(2a + 4)
(-8 + 2a) = 4a + -1a(2a + 4)

Reorder the terms:
-8 + 2a = 4a + -1a(4 + 2a)
-8 + 2a = 4a + (4 * -1a + 2a * -1a)
-8 + 2a = 4a + (-4a + -2a2)

Combine like terms: 4a + -4a = 0
-8 + 2a = 0 + -2a2
-8 + 2a = -2a2

Solving
-8 + 2a = -2a2

Solving for variable 'a'.

Combine like terms: -2a2 + 2a2 = 0
-8 + 2a + 2a2 = 0

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

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

Simplifying
-4 + a + a2 = 0

Solving
-4 + a + a2 = 0

Begin completing the square.

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + a + 4 + a2 = 0 + 4

Reorder the terms:
-4 + 4 + a + a2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + a + a2 = 0 + 4
a + a2 = 0 + 4

Combine like terms: 0 + 4 = 4
a + a2 = 4

The a term is a.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
a + 0.25 + a2 = 4 + 0.25

Reorder the terms:
0.25 + a + a2 = 4 + 0.25

Combine like terms: 4 + 0.25 = 4.25
0.25 + a + a2 = 4.25

Factor a perfect square on the left side:
(a + 0.5)(a + 0.5) = 4.25

Calculate the square root of the right side: 2.061552813

Break this problem into two subproblems by setting 
(a + 0.5) equal to 2.061552813 and -2.061552813.

Subproblem 1
a + 0.5 = 2.061552813

Simplifying
a + 0.5 = 2.061552813

Reorder the terms:
0.5 + a = 2.061552813

Solving
0.5 + a = 2.061552813

Solving for variable 'a'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + a = 2.061552813 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + a = 2.061552813 + -0.5
a = 2.061552813 + -0.5

Combine like terms: 2.061552813 + -0.5 = 1.561552813
a = 1.561552813

Simplifying
a = 1.561552813

Subproblem 2
a + 0.5 = -2.061552813

Simplifying
a + 0.5 = -2.061552813

Reorder the terms:
0.5 + a = -2.061552813

Solving
0.5 + a = -2.061552813

Solving for variable 'a'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + a = -2.061552813 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + a = -2.061552813 + -0.5
a = -2.061552813 + -0.5

Combine like terms: -2.061552813 + -0.5 = -2.561552813
a = -2.561552813

Simplifying
a = -2.561552813

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {1.561552813, -2.561552813}
Solution
a = {1.561552813, -2.561552813}