4(a+2)=2a(a+6)

Solution for 4(a+2)=2a(a+6) equation:

Simplifying
4(a + 2) = 2a(a + 6)

Reorder the terms:
4(2 + a) = 2a(a + 6)
(2 * 4 + a * 4) = 2a(a + 6)
(8 + 4a) = 2a(a + 6)

Reorder the terms:
8 + 4a = 2a(6 + a)
8 + 4a = (6 * 2a + a * 2a)
8 + 4a = (12a + 2a2)

Solving
8 + 4a = 12a + 2a2

Solving for variable 'a'.

Combine like terms: 4a + -12a = -8a
8 + -8a + -2a2 = 12a + 2a2 + -12a + -2a2

Reorder the terms:
8 + -8a + -2a2 = 12a + -12a + 2a2 + -2a2

Combine like terms: 12a + -12a = 0
8 + -8a + -2a2 = 0 + 2a2 + -2a2
8 + -8a + -2a2 = 2a2 + -2a2

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

Factor out the Greatest Common Factor (GCF), '2'.
2(4 + -4a + -1a2) = 0

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

Simplifying
4 + -4a + -1a2 = 0

Solving
4 + -4a + -1a2 = 0

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

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

Move the constant term to the right:

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

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

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

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

The a term is 4a.  Take half its coefficient (2).
Square it (4) and add it to both sides.

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

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

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

Factor a perfect square on the left side:
(a + 2)(a + 2) = 8

Calculate the square root of the right side: 2.828427125

Break this problem into two subproblems by setting 
(a + 2) equal to 2.828427125 and -2.828427125.

Subproblem 1
a + 2 = 2.828427125

Simplifying
a + 2 = 2.828427125

Reorder the terms:
2 + a = 2.828427125

Solving
2 + a = 2.828427125

Solving for variable 'a'.

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

Add '-2' to each side of the equation.
2 + -2 + a = 2.828427125 + -2

Combine like terms: 2 + -2 = 0
0 + a = 2.828427125 + -2
a = 2.828427125 + -2

Combine like terms: 2.828427125 + -2 = 0.828427125
a = 0.828427125

Simplifying
a = 0.828427125

Subproblem 2
a + 2 = -2.828427125

Simplifying
a + 2 = -2.828427125

Reorder the terms:
2 + a = -2.828427125

Solving
2 + a = -2.828427125

Solving for variable 'a'.

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

Add '-2' to each side of the equation.
2 + -2 + a = -2.828427125 + -2

Combine like terms: 2 + -2 = 0
0 + a = -2.828427125 + -2
a = -2.828427125 + -2

Combine like terms: -2.828427125 + -2 = -4.828427125
a = -4.828427125

Simplifying
a = -4.828427125

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {0.828427125, -4.828427125}
Solution
a = {0.828427125, -4.828427125}