3(16-4y)4y=8

Solution for 3(16-4y)4y=8 equation:

Simplifying
3(16 + -4y) * 4y = 8

Reorder the terms for easier multiplication:
3 * 4y(16 + -4y) = 8

Multiply 3 * 4
12y(16 + -4y) = 8
(16 * 12y + -4y * 12y) = 8
(192y + -48y2) = 8

Solving
192y + -48y2 = 8

Solving for variable 'y'.

Reorder the terms:
-8 + 192y + -48y2 = 8 + -8

Combine like terms: 8 + -8 = 0
-8 + 192y + -48y2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(-1 + 24y + -6y2) = 0

Ignore the factor 8.
Subproblem 1
Set the factor '(-1 + 24y + -6y2)' equal to zero and attempt to solve:

Simplifying
-1 + 24y + -6y2 = 0

Solving
-1 + 24y + -6y2 = 0

Begin completing the square.  Divide all terms by
-6 the coefficient of the squared term: 

Divide each side by '-6'.
0.1666666667 + -4y + y2 = 0

Move the constant term to the right:

Add '-0.1666666667' to each side of the equation.
0.1666666667 + -4y + -0.1666666667 + y2 = 0 + -0.1666666667

Reorder the terms:
0.1666666667 + -0.1666666667 + -4y + y2 = 0 + -0.1666666667

Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000
0.0000000000 + -4y + y2 = 0 + -0.1666666667
-4y + y2 = 0 + -0.1666666667

Combine like terms: 0 + -0.1666666667 = -0.1666666667
-4y + y2 = -0.1666666667

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

Add '4' to each side of the equation.
-4y + 4 + y2 = -0.1666666667 + 4

Reorder the terms:
4 + -4y + y2 = -0.1666666667 + 4

Combine like terms: -0.1666666667 + 4 = 3.8333333333
4 + -4y + y2 = 3.8333333333

Factor a perfect square on the left side:
(y + -2)(y + -2) = 3.8333333333

Calculate the square root of the right side: 1.957890021

Break this problem into two subproblems by setting 
(y + -2) equal to 1.957890021 and -1.957890021.

Subproblem 1
y + -2 = 1.957890021

Simplifying
y + -2 = 1.957890021

Reorder the terms:
-2 + y = 1.957890021

Solving
-2 + y = 1.957890021

Solving for variable 'y'.

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

Add '2' to each side of the equation.
-2 + 2 + y = 1.957890021 + 2

Combine like terms: -2 + 2 = 0
0 + y = 1.957890021 + 2
y = 1.957890021 + 2

Combine like terms: 1.957890021 + 2 = 3.957890021
y = 3.957890021

Simplifying
y = 3.957890021

Subproblem 2
y + -2 = -1.957890021

Simplifying
y + -2 = -1.957890021

Reorder the terms:
-2 + y = -1.957890021

Solving
-2 + y = -1.957890021

Solving for variable 'y'.

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

Add '2' to each side of the equation.
-2 + 2 + y = -1.957890021 + 2

Combine like terms: -2 + 2 = 0
0 + y = -1.957890021 + 2
y = -1.957890021 + 2

Combine like terms: -1.957890021 + 2 = 0.042109979
y = 0.042109979

Simplifying
y = 0.042109979

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {3.957890021, 0.042109979}
Solution
y = {3.957890021, 0.042109979}