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

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

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

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

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

Multiply 3 * 2
6y(-1 + 2y) = -3
(-1 * 6y + 2y * 6y) = -3
(-6y + 12y2) = -3

Solving
-6y + 12y2 = -3

Solving for variable 'y'.

Reorder the terms:
3 + -6y + 12y2 = -3 + 3

Combine like terms: -3 + 3 = 0
3 + -6y + 12y2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(1 + -2y + 4y2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(1 + -2y + 4y2)' equal to zero and attempt to solve:

Simplifying
1 + -2y + 4y2 = 0

Solving
1 + -2y + 4y2 = 0

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

Divide each side by '4'.
0.25 + -0.5y + y2 = 0

Move the constant term to the right:

Add '-0.25' to each side of the equation.
0.25 + -0.5y + -0.25 + y2 = 0 + -0.25

Reorder the terms:
0.25 + -0.25 + -0.5y + y2 = 0 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + -0.5y + y2 = 0 + -0.25
-0.5y + y2 = 0 + -0.25

Combine like terms: 0 + -0.25 = -0.25
-0.5y + y2 = -0.25

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 = -0.25 + 0.0625

Reorder the terms:
0.0625 + -0.5y + y2 = -0.25 + 0.0625

Combine like terms: -0.25 + 0.0625 = -0.1875
0.0625 + -0.5y + y2 = -0.1875

Factor a perfect square on the left side:
(y + -0.25)(y + -0.25) = -0.1875

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.