3y(2y-4)=16

Solution for 3y(2y-4)=16 equation:

Simplifying
3y(2y + -4) = 16

Reorder the terms:
3y(-4 + 2y) = 16
(-4 * 3y + 2y * 3y) = 16
(-12y + 6y2) = 16

Solving
-12y + 6y2 = 16

Solving for variable 'y'.

Reorder the terms:
-16 + -12y + 6y2 = 16 + -16

Combine like terms: 16 + -16 = 0
-16 + -12y + 6y2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-8 + -6y + 3y2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-8 + -6y + 3y2)' equal to zero and attempt to solve:

Simplifying
-8 + -6y + 3y2 = 0

Solving
-8 + -6y + 3y2 = 0

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

Divide each side by '3'.
-2.666666667 + -2y + y2 = 0

Move the constant term to the right:

Add '2.666666667' to each side of the equation.
-2.666666667 + -2y + 2.666666667 + y2 = 0 + 2.666666667

Reorder the terms:
-2.666666667 + 2.666666667 + -2y + y2 = 0 + 2.666666667

Combine like terms: -2.666666667 + 2.666666667 = 0.000000000
0.000000000 + -2y + y2 = 0 + 2.666666667
-2y + y2 = 0 + 2.666666667

Combine like terms: 0 + 2.666666667 = 2.666666667
-2y + y2 = 2.666666667

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

Add '1' to each side of the equation.
-2y + 1 + y2 = 2.666666667 + 1

Reorder the terms:
1 + -2y + y2 = 2.666666667 + 1

Combine like terms: 2.666666667 + 1 = 3.666666667
1 + -2y + y2 = 3.666666667

Factor a perfect square on the left side:
(y + -1)(y + -1) = 3.666666667

Calculate the square root of the right side: 1.914854216

Break this problem into two subproblems by setting 
(y + -1) equal to 1.914854216 and -1.914854216.

Subproblem 1
y + -1 = 1.914854216

Simplifying
y + -1 = 1.914854216

Reorder the terms:
-1 + y = 1.914854216

Solving
-1 + y = 1.914854216

Solving for variable 'y'.

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

Add '1' to each side of the equation.
-1 + 1 + y = 1.914854216 + 1

Combine like terms: -1 + 1 = 0
0 + y = 1.914854216 + 1
y = 1.914854216 + 1

Combine like terms: 1.914854216 + 1 = 2.914854216
y = 2.914854216

Simplifying
y = 2.914854216

Subproblem 2
y + -1 = -1.914854216

Simplifying
y + -1 = -1.914854216

Reorder the terms:
-1 + y = -1.914854216

Solving
-1 + y = -1.914854216

Solving for variable 'y'.

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

Add '1' to each side of the equation.
-1 + 1 + y = -1.914854216 + 1

Combine like terms: -1 + 1 = 0
0 + y = -1.914854216 + 1
y = -1.914854216 + 1

Combine like terms: -1.914854216 + 1 = -0.914854216
y = -0.914854216

Simplifying
y = -0.914854216

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {2.914854216, -0.914854216}
Solution
y = {2.914854216, -0.914854216}