3(2a+4)a=3

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

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

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

Reorder the terms for easier multiplication:
3a(4 + 2a) = 3
(4 * 3a + 2a * 3a) = 3
(12a + 6a2) = 3

Solving
12a + 6a2 = 3

Solving for variable 'a'.

Reorder the terms:
-3 + 12a + 6a2 = 3 + -3

Combine like terms: 3 + -3 = 0
-3 + 12a + 6a2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-1 + 4a + 2a2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-1 + 4a + 2a2)' equal to zero and attempt to solve:

Simplifying
-1 + 4a + 2a2 = 0

Solving
-1 + 4a + 2a2 = 0

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

Divide each side by '2'.
-0.5 + 2a + a2 = 0

Move the constant term to the right:

Add '0.5' to each side of the equation.
-0.5 + 2a + 0.5 + a2 = 0 + 0.5

Reorder the terms:
-0.5 + 0.5 + 2a + a2 = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + 2a + a2 = 0 + 0.5
2a + a2 = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5
2a + a2 = 0.5

The a term is 2a.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2a + 1 + a2 = 0.5 + 1

Reorder the terms:
1 + 2a + a2 = 0.5 + 1

Combine like terms: 0.5 + 1 = 1.5
1 + 2a + a2 = 1.5

Factor a perfect square on the left side:
(a + 1)(a + 1) = 1.5

Calculate the square root of the right side: 1.224744871

Break this problem into two subproblems by setting 
(a + 1) equal to 1.224744871 and -1.224744871.

Subproblem 1
a + 1 = 1.224744871

Simplifying
a + 1 = 1.224744871

Reorder the terms:
1 + a = 1.224744871

Solving
1 + a = 1.224744871

Solving for variable 'a'.

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

Add '-1' to each side of the equation.
1 + -1 + a = 1.224744871 + -1

Combine like terms: 1 + -1 = 0
0 + a = 1.224744871 + -1
a = 1.224744871 + -1

Combine like terms: 1.224744871 + -1 = 0.224744871
a = 0.224744871

Simplifying
a = 0.224744871

Subproblem 2
a + 1 = -1.224744871

Simplifying
a + 1 = -1.224744871

Reorder the terms:
1 + a = -1.224744871

Solving
1 + a = -1.224744871

Solving for variable 'a'.

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

Add '-1' to each side of the equation.
1 + -1 + a = -1.224744871 + -1

Combine like terms: 1 + -1 = 0
0 + a = -1.224744871 + -1
a = -1.224744871 + -1

Combine like terms: -1.224744871 + -1 = -2.224744871
a = -2.224744871

Simplifying
a = -2.224744871

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {0.224744871, -2.224744871}
Solution
a = {0.224744871, -2.224744871}