4(2y-1)02(3y)=1

Solution for 4(2y-1)02(3y)=1 equation:

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

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

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

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

Multiply 4 * 2
8 * 3y(-1 + 2y) = 1

Multiply 8 * 3
24y(-1 + 2y) = 1
(-1 * 24y + 2y * 24y) = 1
(-24y + 48y2) = 1

Solving
-24y + 48y2 = 1

Solving for variable 'y'.

Reorder the terms:
-1 + -24y + 48y2 = 1 + -1

Combine like terms: 1 + -1 = 0
-1 + -24y + 48y2 = 0

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

Divide each side by '48'.
-0.02083333333 + -0.5y + y2 = 0

Move the constant term to the right:

Add '0.02083333333' to each side of the equation.
-0.02083333333 + -0.5y + 0.02083333333 + y2 = 0 + 0.02083333333

Reorder the terms:
-0.02083333333 + 0.02083333333 + -0.5y + y2 = 0 + 0.02083333333

Combine like terms: -0.02083333333 + 0.02083333333 = 0.00000000000
0.00000000000 + -0.5y + y2 = 0 + 0.02083333333
-0.5y + y2 = 0 + 0.02083333333

Combine like terms: 0 + 0.02083333333 = 0.02083333333
-0.5y + y2 = 0.02083333333

The y term is -0.5y.  Take half its coefficient (-0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
-0.5y + 0.0625 + y2 = 0.02083333333 + 0.0625

Reorder the terms:
0.0625 + -0.5y + y2 = 0.02083333333 + 0.0625

Combine like terms: 0.02083333333 + 0.0625 = 0.08333333333
0.0625 + -0.5y + y2 = 0.08333333333

Factor a perfect square on the left side:
(y + -0.25)(y + -0.25) = 0.08333333333

Calculate the square root of the right side: 0.288675135

Break this problem into two subproblems by setting 
(y + -0.25) equal to 0.288675135 and -0.288675135.

Subproblem 1
y + -0.25 = 0.288675135

Simplifying
y + -0.25 = 0.288675135

Reorder the terms:
-0.25 + y = 0.288675135

Solving
-0.25 + y = 0.288675135

Solving for variable 'y'.

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

Add '0.25' to each side of the equation.
-0.25 + 0.25 + y = 0.288675135 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + y = 0.288675135 + 0.25
y = 0.288675135 + 0.25

Combine like terms: 0.288675135 + 0.25 = 0.538675135
y = 0.538675135

Simplifying
y = 0.538675135

Subproblem 2
y + -0.25 = -0.288675135

Simplifying
y + -0.25 = -0.288675135

Reorder the terms:
-0.25 + y = -0.288675135

Solving
-0.25 + y = -0.288675135

Solving for variable 'y'.

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

Add '0.25' to each side of the equation.
-0.25 + 0.25 + y = -0.288675135 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + y = -0.288675135 + 0.25
y = -0.288675135 + 0.25

Combine like terms: -0.288675135 + 0.25 = -0.038675135
y = -0.038675135

Simplifying
y = -0.038675135

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {0.538675135, -0.038675135}