3(3y-1)03(2y)=4

Solution for 3(3y-1)03(2y)=4 equation:

Simplifying
3(3y + -1) * 3(2y) = 4

Reorder the terms:
3(-1 + 3y) * 3(2y) = 4

Remove parenthesis around (2y)
3(-1 + 3y) * 3 * 2y = 4

Reorder the terms for easier multiplication:
3 * 3 * 2y(-1 + 3y) = 4

Multiply 3 * 3
9 * 2y(-1 + 3y) = 4

Multiply 9 * 2
18y(-1 + 3y) = 4
(-1 * 18y + 3y * 18y) = 4
(-18y + 54y2) = 4

Solving
-18y + 54y2 = 4

Solving for variable 'y'.

Reorder the terms:
-4 + -18y + 54y2 = 4 + -4

Combine like terms: 4 + -4 = 0
-4 + -18y + 54y2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-2 + -9y + 27y2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-2 + -9y + 27y2)' equal to zero and attempt to solve:

Simplifying
-2 + -9y + 27y2 = 0

Solving
-2 + -9y + 27y2 = 0

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

Divide each side by '27'.
-0.07407407407 + -0.3333333333y + y2 = 0

Move the constant term to the right:

Add '0.07407407407' to each side of the equation.
-0.07407407407 + -0.3333333333y + 0.07407407407 + y2 = 0 + 0.07407407407

Reorder the terms:
-0.07407407407 + 0.07407407407 + -0.3333333333y + y2 = 0 + 0.07407407407

Combine like terms: -0.07407407407 + 0.07407407407 = 0.00000000000
0.00000000000 + -0.3333333333y + y2 = 0 + 0.07407407407
-0.3333333333y + y2 = 0 + 0.07407407407

Combine like terms: 0 + 0.07407407407 = 0.07407407407
-0.3333333333y + y2 = 0.07407407407

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 = 0.07407407407 + 0.02777777779

Reorder the terms:
0.02777777779 + -0.3333333333y + y2 = 0.07407407407 + 0.02777777779

Combine like terms: 0.07407407407 + 0.02777777779 = 0.10185185186
0.02777777779 + -0.3333333333y + y2 = 0.10185185186

Factor a perfect square on the left side:
(y + -0.1666666667)(y + -0.1666666667) = 0.10185185186

Calculate the square root of the right side: 0.319142369

Break this problem into two subproblems by setting 
(y + -0.1666666667) equal to 0.319142369 and -0.319142369.

Subproblem 1
y + -0.1666666667 = 0.319142369

Simplifying
y + -0.1666666667 = 0.319142369

Reorder the terms:
-0.1666666667 + y = 0.319142369

Solving
-0.1666666667 + y = 0.319142369

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 = 0.319142369 + 0.1666666667

Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000
0.0000000000 + y = 0.319142369 + 0.1666666667
y = 0.319142369 + 0.1666666667

Combine like terms: 0.319142369 + 0.1666666667 = 0.4858090357
y = 0.4858090357

Simplifying
y = 0.4858090357

Subproblem 2
y + -0.1666666667 = -0.319142369

Simplifying
y + -0.1666666667 = -0.319142369

Reorder the terms:
-0.1666666667 + y = -0.319142369

Solving
-0.1666666667 + y = -0.319142369

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 = -0.319142369 + 0.1666666667

Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000
0.0000000000 + y = -0.319142369 + 0.1666666667
y = -0.319142369 + 0.1666666667

Combine like terms: -0.319142369 + 0.1666666667 = -0.1524757023
y = -0.1524757023

Simplifying
y = -0.1524757023

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {0.4858090357, -0.1524757023}
Solution
y = {0.4858090357, -0.1524757023}