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

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

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

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

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

Reorder the terms:
-8a + 2a2 = -4 + 4a + -2a

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

Solving
-8a + 2a2 = -4 + 2a

Solving for variable 'a'.

Reorder the terms:
4 + -8a + -2a + 2a2 = -4 + 2a + 4 + -2a

Combine like terms: -8a + -2a = -10a
4 + -10a + 2a2 = -4 + 2a + 4 + -2a

Reorder the terms:
4 + -10a + 2a2 = -4 + 4 + 2a + -2a

Combine like terms: -4 + 4 = 0
4 + -10a + 2a2 = 0 + 2a + -2a
4 + -10a + 2a2 = 2a + -2a

Combine like terms: 2a + -2a = 0
4 + -10a + 2a2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(2 + -5a + a2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(2 + -5a + a2)' equal to zero and attempt to solve:

Simplifying
2 + -5a + a2 = 0

Solving
2 + -5a + a2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + -5a + -2 + a2 = 0 + -2

Reorder the terms:
2 + -2 + -5a + a2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -5a + a2 = 0 + -2
-5a + a2 = 0 + -2

Combine like terms: 0 + -2 = -2
-5a + a2 = -2

The a term is -5a.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5a + 6.25 + a2 = -2 + 6.25

Reorder the terms:
6.25 + -5a + a2 = -2 + 6.25

Combine like terms: -2 + 6.25 = 4.25
6.25 + -5a + a2 = 4.25

Factor a perfect square on the left side:
(a + -2.5)(a + -2.5) = 4.25

Calculate the square root of the right side: 2.061552813

Break this problem into two subproblems by setting 
(a + -2.5) equal to 2.061552813 and -2.061552813.

Subproblem 1
a + -2.5 = 2.061552813

Simplifying
a + -2.5 = 2.061552813

Reorder the terms:
-2.5 + a = 2.061552813

Solving
-2.5 + a = 2.061552813

Solving for variable 'a'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + a = 2.061552813 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + a = 2.061552813 + 2.5
a = 2.061552813 + 2.5

Combine like terms: 2.061552813 + 2.5 = 4.561552813
a = 4.561552813

Simplifying
a = 4.561552813

Subproblem 2
a + -2.5 = -2.061552813

Simplifying
a + -2.5 = -2.061552813

Reorder the terms:
-2.5 + a = -2.061552813

Solving
-2.5 + a = -2.061552813

Solving for variable 'a'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + a = -2.061552813 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + a = -2.061552813 + 2.5
a = -2.061552813 + 2.5

Combine like terms: -2.061552813 + 2.5 = 0.438447187
a = 0.438447187

Simplifying
a = 0.438447187

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {4.561552813, 0.438447187}
Solution
a = {4.561552813, 0.438447187}