4y(3y-2)-6=-3y(1-y)

Solution for 4y(3y-2)-6=-3y(1-y) equation:

Simplifying
4y(3y + -2) + -6 = -3y(1 + -1y)

Reorder the terms:
4y(-2 + 3y) + -6 = -3y(1 + -1y)
(-2 * 4y + 3y * 4y) + -6 = -3y(1 + -1y)
(-8y + 12y2) + -6 = -3y(1 + -1y)

Reorder the terms:
-6 + -8y + 12y2 = -3y(1 + -1y)
-6 + -8y + 12y2 = (1 * -3y + -1y * -3y)
-6 + -8y + 12y2 = (-3y + 3y2)

Solving
-6 + -8y + 12y2 = -3y + 3y2

Solving for variable 'y'.

Reorder the terms:
-6 + -8y + 3y + 12y2 + -3y2 = -3y + 3y2 + 3y + -3y2

Combine like terms: -8y + 3y = -5y
-6 + -5y + 12y2 + -3y2 = -3y + 3y2 + 3y + -3y2

Combine like terms: 12y2 + -3y2 = 9y2
-6 + -5y + 9y2 = -3y + 3y2 + 3y + -3y2

Reorder the terms:
-6 + -5y + 9y2 = -3y + 3y + 3y2 + -3y2

Combine like terms: -3y + 3y = 0
-6 + -5y + 9y2 = 0 + 3y2 + -3y2
-6 + -5y + 9y2 = 3y2 + -3y2

Combine like terms: 3y2 + -3y2 = 0
-6 + -5y + 9y2 = 0

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

Divide each side by '9'.
-0.6666666667 + -0.5555555556y + y2 = 0

Move the constant term to the right:

Add '0.6666666667' to each side of the equation.
-0.6666666667 + -0.5555555556y + 0.6666666667 + y2 = 0 + 0.6666666667

Reorder the terms:
-0.6666666667 + 0.6666666667 + -0.5555555556y + y2 = 0 + 0.6666666667

Combine like terms: -0.6666666667 + 0.6666666667 = 0.0000000000
0.0000000000 + -0.5555555556y + y2 = 0 + 0.6666666667
-0.5555555556y + y2 = 0 + 0.6666666667

Combine like terms: 0 + 0.6666666667 = 0.6666666667
-0.5555555556y + y2 = 0.6666666667

The y term is -0.5555555556y.  Take half its coefficient (-0.2777777778).
Square it (0.07716049384) and add it to both sides.

Add '0.07716049384' to each side of the equation.
-0.5555555556y + 0.07716049384 + y2 = 0.6666666667 + 0.07716049384

Reorder the terms:
0.07716049384 + -0.5555555556y + y2 = 0.6666666667 + 0.07716049384

Combine like terms: 0.6666666667 + 0.07716049384 = 0.74382716054
0.07716049384 + -0.5555555556y + y2 = 0.74382716054

Factor a perfect square on the left side:
(y + -0.2777777778)(y + -0.2777777778) = 0.74382716054

Calculate the square root of the right side: 0.86245415

Break this problem into two subproblems by setting 
(y + -0.2777777778) equal to 0.86245415 and -0.86245415.

Subproblem 1
y + -0.2777777778 = 0.86245415

Simplifying
y + -0.2777777778 = 0.86245415

Reorder the terms:
-0.2777777778 + y = 0.86245415

Solving
-0.2777777778 + y = 0.86245415

Solving for variable 'y'.

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

Add '0.2777777778' to each side of the equation.
-0.2777777778 + 0.2777777778 + y = 0.86245415 + 0.2777777778

Combine like terms: -0.2777777778 + 0.2777777778 = 0.0000000000
0.0000000000 + y = 0.86245415 + 0.2777777778
y = 0.86245415 + 0.2777777778

Combine like terms: 0.86245415 + 0.2777777778 = 1.1402319278
y = 1.1402319278

Simplifying
y = 1.1402319278

Subproblem 2
y + -0.2777777778 = -0.86245415

Simplifying
y + -0.2777777778 = -0.86245415

Reorder the terms:
-0.2777777778 + y = -0.86245415

Solving
-0.2777777778 + y = -0.86245415

Solving for variable 'y'.

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

Add '0.2777777778' to each side of the equation.
-0.2777777778 + 0.2777777778 + y = -0.86245415 + 0.2777777778

Combine like terms: -0.2777777778 + 0.2777777778 = 0.0000000000
0.0000000000 + y = -0.86245415 + 0.2777777778
y = -0.86245415 + 0.2777777778

Combine like terms: -0.86245415 + 0.2777777778 = -0.5846763722
y = -0.5846763722

Simplifying
y = -0.5846763722

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {1.1402319278, -0.5846763722}