5(3y-1)3(2y)=16

Solution for 5(3y-1)3(2y)=16 equation:

Simplifying
5(3y + -1) * 3(2y) = 16

Reorder the terms:
5(-1 + 3y) * 3(2y) = 16

Remove parenthesis around (2y)
5(-1 + 3y) * 3 * 2y = 16

Reorder the terms for easier multiplication:
5 * 3 * 2y(-1 + 3y) = 16

Multiply 5 * 3
15 * 2y(-1 + 3y) = 16

Multiply 15 * 2
30y(-1 + 3y) = 16
(-1 * 30y + 3y * 30y) = 16
(-30y + 90y2) = 16

Solving
-30y + 90y2 = 16

Solving for variable 'y'.

Reorder the terms:
-16 + -30y + 90y2 = 16 + -16

Combine like terms: 16 + -16 = 0
-16 + -30y + 90y2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-8 + -15y + 45y2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-8 + -15y + 45y2)' equal to zero and attempt to solve:

Simplifying
-8 + -15y + 45y2 = 0

Solving
-8 + -15y + 45y2 = 0

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

Divide each side by '45'.
-0.1777777778 + -0.3333333333y + y2 = 0

Move the constant term to the right:

Add '0.1777777778' to each side of the equation.
-0.1777777778 + -0.3333333333y + 0.1777777778 + y2 = 0 + 0.1777777778

Reorder the terms:
-0.1777777778 + 0.1777777778 + -0.3333333333y + y2 = 0 + 0.1777777778

Combine like terms: -0.1777777778 + 0.1777777778 = 0.0000000000
0.0000000000 + -0.3333333333y + y2 = 0 + 0.1777777778
-0.3333333333y + y2 = 0 + 0.1777777778

Combine like terms: 0 + 0.1777777778 = 0.1777777778
-0.3333333333y + y2 = 0.1777777778

The y term is -0.3333333333y.  Take half its coefficient (-0.1666666667).
Square it (0.02777777779) and add it to both sides.

Add '0.02777777779' to each side of the equation.
-0.3333333333y + 0.02777777779 + y2 = 0.1777777778 + 0.02777777779

Reorder the terms:
0.02777777779 + -0.3333333333y + y2 = 0.1777777778 + 0.02777777779

Combine like terms: 0.1777777778 + 0.02777777779 = 0.20555555559
0.02777777779 + -0.3333333333y + y2 = 0.20555555559

Factor a perfect square on the left side:
(y + -0.1666666667)(y + -0.1666666667) = 0.20555555559

Calculate the square root of the right side: 0.45338235

Break this problem into two subproblems by setting 
(y + -0.1666666667) equal to 0.45338235 and -0.45338235.

Subproblem 1
y + -0.1666666667 = 0.45338235

Simplifying
y + -0.1666666667 = 0.45338235

Reorder the terms:
-0.1666666667 + y = 0.45338235

Solving
-0.1666666667 + y = 0.45338235

Solving for variable 'y'.

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

Add '0.1666666667' to each side of the equation.
-0.1666666667 + 0.1666666667 + y = 0.45338235 + 0.1666666667

Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000
0.0000000000 + y = 0.45338235 + 0.1666666667
y = 0.45338235 + 0.1666666667

Combine like terms: 0.45338235 + 0.1666666667 = 0.6200490167
y = 0.6200490167

Simplifying
y = 0.6200490167

Subproblem 2
y + -0.1666666667 = -0.45338235

Simplifying
y + -0.1666666667 = -0.45338235

Reorder the terms:
-0.1666666667 + y = -0.45338235

Solving
-0.1666666667 + y = -0.45338235

Solving for variable 'y'.

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

Add '0.1666666667' to each side of the equation.
-0.1666666667 + 0.1666666667 + y = -0.45338235 + 0.1666666667

Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000
0.0000000000 + y = -0.45338235 + 0.1666666667
y = -0.45338235 + 0.1666666667

Combine like terms: -0.45338235 + 0.1666666667 = -0.2867156833
y = -0.2867156833

Simplifying
y = -0.2867156833

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {0.6200490167, -0.2867156833}
Solution
y = {0.6200490167, -0.2867156833}