3(12+4y)2y=6

Solution for 3(12+4y)2y=6 equation:

Simplifying
3(12 + 4y) * 2y = 6

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

Multiply 3 * 2
6y(12 + 4y) = 6
(12 * 6y + 4y * 6y) = 6
(72y + 24y2) = 6

Solving
72y + 24y2 = 6

Solving for variable 'y'.

Reorder the terms:
-6 + 72y + 24y2 = 6 + -6

Combine like terms: 6 + -6 = 0
-6 + 72y + 24y2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(-1 + 12y + 4y2) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(-1 + 12y + 4y2)' equal to zero and attempt to solve:

Simplifying
-1 + 12y + 4y2 = 0

Solving
-1 + 12y + 4y2 = 0

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

Divide each side by '4'.
-0.25 + 3y + y2 = 0

Move the constant term to the right:

Add '0.25' to each side of the equation.
-0.25 + 3y + 0.25 + y2 = 0 + 0.25

Reorder the terms:
-0.25 + 0.25 + 3y + y2 = 0 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + 3y + y2 = 0 + 0.25
3y + y2 = 0 + 0.25

Combine like terms: 0 + 0.25 = 0.25
3y + y2 = 0.25

The y term is 3y.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3y + 2.25 + y2 = 0.25 + 2.25

Reorder the terms:
2.25 + 3y + y2 = 0.25 + 2.25

Combine like terms: 0.25 + 2.25 = 2.5
2.25 + 3y + y2 = 2.5

Factor a perfect square on the left side:
(y + 1.5)(y + 1.5) = 2.5

Calculate the square root of the right side: 1.58113883

Break this problem into two subproblems by setting 
(y + 1.5) equal to 1.58113883 and -1.58113883.

Subproblem 1
y + 1.5 = 1.58113883

Simplifying
y + 1.5 = 1.58113883

Reorder the terms:
1.5 + y = 1.58113883

Solving
1.5 + y = 1.58113883

Solving for variable 'y'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + y = 1.58113883 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + y = 1.58113883 + -1.5
y = 1.58113883 + -1.5

Combine like terms: 1.58113883 + -1.5 = 0.08113883
y = 0.08113883

Simplifying
y = 0.08113883

Subproblem 2
y + 1.5 = -1.58113883

Simplifying
y + 1.5 = -1.58113883

Reorder the terms:
1.5 + y = -1.58113883

Solving
1.5 + y = -1.58113883

Solving for variable 'y'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + y = -1.58113883 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + y = -1.58113883 + -1.5
y = -1.58113883 + -1.5

Combine like terms: -1.58113883 + -1.5 = -3.08113883
y = -3.08113883

Simplifying
y = -3.08113883

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {0.08113883, -3.08113883}
Solution
y = {0.08113883, -3.08113883}