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

Solution for 2(a-2)=((a-1)(a-4)) equation:

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

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

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

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

Multiply (-1 + a) * (-4 + a)
-4 + 2a = ((-1(-4 + a) + a(-4 + a)))
-4 + 2a = (((-4 * -1 + a * -1) + a(-4 + a)))
-4 + 2a = (((4 + -1a) + a(-4 + a)))
-4 + 2a = ((4 + -1a + (-4 * a + a * a)))
-4 + 2a = ((4 + -1a + (-4a + a2)))

Combine like terms: -1a + -4a = -5a
-4 + 2a = ((4 + -5a + a2))
-4 + 2a = (4 + -5a + a2)

Remove parenthesis around (4 + -5a + a2)
-4 + 2a = 4 + -5a + a2

Solving
-4 + 2a = 4 + -5a + a2

Solving for variable 'a'.

Reorder the terms:
-4 + -4 + 2a + 5a + -1a2 = 4 + -5a + a2 + -4 + 5a + -1a2

Combine like terms: -4 + -4 = -8
-8 + 2a + 5a + -1a2 = 4 + -5a + a2 + -4 + 5a + -1a2

Combine like terms: 2a + 5a = 7a
-8 + 7a + -1a2 = 4 + -5a + a2 + -4 + 5a + -1a2

Reorder the terms:
-8 + 7a + -1a2 = 4 + -4 + -5a + 5a + a2 + -1a2

Combine like terms: 4 + -4 = 0
-8 + 7a + -1a2 = 0 + -5a + 5a + a2 + -1a2
-8 + 7a + -1a2 = -5a + 5a + a2 + -1a2

Combine like terms: -5a + 5a = 0
-8 + 7a + -1a2 = 0 + a2 + -1a2
-8 + 7a + -1a2 = a2 + -1a2

Combine like terms: a2 + -1a2 = 0
-8 + 7a + -1a2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
8 + -7a + a2 = 0

Move the constant term to the right:

Add '-8' to each side of the equation.
8 + -7a + -8 + a2 = 0 + -8

Reorder the terms:
8 + -8 + -7a + a2 = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -7a + a2 = 0 + -8
-7a + a2 = 0 + -8

Combine like terms: 0 + -8 = -8
-7a + a2 = -8

The a term is -7a.  Take half its coefficient (-3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
-7a + 12.25 + a2 = -8 + 12.25

Reorder the terms:
12.25 + -7a + a2 = -8 + 12.25

Combine like terms: -8 + 12.25 = 4.25
12.25 + -7a + a2 = 4.25

Factor a perfect square on the left side:
(a + -3.5)(a + -3.5) = 4.25

Calculate the square root of the right side: 2.061552813

Break this problem into two subproblems by setting 
(a + -3.5) equal to 2.061552813 and -2.061552813.

Subproblem 1
a + -3.5 = 2.061552813

Simplifying
a + -3.5 = 2.061552813

Reorder the terms:
-3.5 + a = 2.061552813

Solving
-3.5 + a = 2.061552813

Solving for variable 'a'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + a = 2.061552813 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + a = 2.061552813 + 3.5
a = 2.061552813 + 3.5

Combine like terms: 2.061552813 + 3.5 = 5.561552813
a = 5.561552813

Simplifying
a = 5.561552813

Subproblem 2
a + -3.5 = -2.061552813

Simplifying
a + -3.5 = -2.061552813

Reorder the terms:
-3.5 + a = -2.061552813

Solving
-3.5 + a = -2.061552813

Solving for variable 'a'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + a = -2.061552813 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + a = -2.061552813 + 3.5
a = -2.061552813 + 3.5

Combine like terms: -2.061552813 + 3.5 = 1.438447187
a = 1.438447187

Simplifying
a = 1.438447187

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {5.561552813, 1.438447187}