3(4a+2)=2a(a-2)

Solution for 3(4a+2)=2a(a-2) equation:

Simplifying
3(4a + 2) = 2a(a + -2)

Reorder the terms:
3(2 + 4a) = 2a(a + -2)
(2 * 3 + 4a * 3) = 2a(a + -2)
(6 + 12a) = 2a(a + -2)

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

Solving
6 + 12a = -4a + 2a2

Solving for variable 'a'.

Combine like terms: 12a + 4a = 16a
6 + 16a + -2a2 = -4a + 2a2 + 4a + -2a2

Reorder the terms:
6 + 16a + -2a2 = -4a + 4a + 2a2 + -2a2

Combine like terms: -4a + 4a = 0
6 + 16a + -2a2 = 0 + 2a2 + -2a2
6 + 16a + -2a2 = 2a2 + -2a2

Combine like terms: 2a2 + -2a2 = 0
6 + 16a + -2a2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + 8a + -1a2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(3 + 8a + -1a2)' equal to zero and attempt to solve:

Simplifying
3 + 8a + -1a2 = 0

Solving
3 + 8a + -1a2 = 0

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

Divide each side by '-1'.
-3 + -8a + a2 = 0

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + -8a + 3 + a2 = 0 + 3

Reorder the terms:
-3 + 3 + -8a + a2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -8a + a2 = 0 + 3
-8a + a2 = 0 + 3

Combine like terms: 0 + 3 = 3
-8a + a2 = 3

The a term is -8a.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8a + 16 + a2 = 3 + 16

Reorder the terms:
16 + -8a + a2 = 3 + 16

Combine like terms: 3 + 16 = 19
16 + -8a + a2 = 19

Factor a perfect square on the left side:
(a + -4)(a + -4) = 19

Calculate the square root of the right side: 4.358898944

Break this problem into two subproblems by setting 
(a + -4) equal to 4.358898944 and -4.358898944.

Subproblem 1
a + -4 = 4.358898944

Simplifying
a + -4 = 4.358898944

Reorder the terms:
-4 + a = 4.358898944

Solving
-4 + a = 4.358898944

Solving for variable 'a'.

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

Add '4' to each side of the equation.
-4 + 4 + a = 4.358898944 + 4

Combine like terms: -4 + 4 = 0
0 + a = 4.358898944 + 4
a = 4.358898944 + 4

Combine like terms: 4.358898944 + 4 = 8.358898944
a = 8.358898944

Simplifying
a = 8.358898944

Subproblem 2
a + -4 = -4.358898944

Simplifying
a + -4 = -4.358898944

Reorder the terms:
-4 + a = -4.358898944

Solving
-4 + a = -4.358898944

Solving for variable 'a'.

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

Add '4' to each side of the equation.
-4 + 4 + a = -4.358898944 + 4

Combine like terms: -4 + 4 = 0
0 + a = -4.358898944 + 4
a = -4.358898944 + 4

Combine like terms: -4.358898944 + 4 = -0.358898944
a = -0.358898944

Simplifying
a = -0.358898944

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {8.358898944, -0.358898944}
Solution
a = {8.358898944, -0.358898944}