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

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

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

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

Multiply -4 * 3
-12y(2 + -1y) = 3(y + -4)
(2 * -12y + -1y * -12y) = 3(y + -4)
(-24y + 12y2) = 3(y + -4)

Reorder the terms:
-24y + 12y2 = 3(-4 + y)
-24y + 12y2 = (-4 * 3 + y * 3)
-24y + 12y2 = (-12 + 3y)

Solving
-24y + 12y2 = -12 + 3y

Solving for variable 'y'.

Reorder the terms:
12 + -24y + -3y + 12y2 = -12 + 3y + 12 + -3y

Combine like terms: -24y + -3y = -27y
12 + -27y + 12y2 = -12 + 3y + 12 + -3y

Reorder the terms:
12 + -27y + 12y2 = -12 + 12 + 3y + -3y

Combine like terms: -12 + 12 = 0
12 + -27y + 12y2 = 0 + 3y + -3y
12 + -27y + 12y2 = 3y + -3y

Combine like terms: 3y + -3y = 0
12 + -27y + 12y2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(4 + -9y + 4y2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(4 + -9y + 4y2)' equal to zero and attempt to solve:

Simplifying
4 + -9y + 4y2 = 0

Solving
4 + -9y + 4y2 = 0

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

Divide each side by '4'.
1 + -2.25y + y2 = 0

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + -2.25y + -1 + y2 = 0 + -1

Reorder the terms:
1 + -1 + -2.25y + y2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2.25y + y2 = 0 + -1
-2.25y + y2 = 0 + -1

Combine like terms: 0 + -1 = -1
-2.25y + y2 = -1

The y term is -2.25y.  Take half its coefficient (-1.125).
Square it (1.265625) and add it to both sides.

Add '1.265625' to each side of the equation.
-2.25y + 1.265625 + y2 = -1 + 1.265625

Reorder the terms:
1.265625 + -2.25y + y2 = -1 + 1.265625

Combine like terms: -1 + 1.265625 = 0.265625
1.265625 + -2.25y + y2 = 0.265625

Factor a perfect square on the left side:
(y + -1.125)(y + -1.125) = 0.265625

Calculate the square root of the right side: 0.515388203

Break this problem into two subproblems by setting 
(y + -1.125) equal to 0.515388203 and -0.515388203.

Subproblem 1
y + -1.125 = 0.515388203

Simplifying
y + -1.125 = 0.515388203

Reorder the terms:
-1.125 + y = 0.515388203

Solving
-1.125 + y = 0.515388203

Solving for variable 'y'.

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

Add '1.125' to each side of the equation.
-1.125 + 1.125 + y = 0.515388203 + 1.125

Combine like terms: -1.125 + 1.125 = 0.000
0.000 + y = 0.515388203 + 1.125
y = 0.515388203 + 1.125

Combine like terms: 0.515388203 + 1.125 = 1.640388203
y = 1.640388203

Simplifying
y = 1.640388203

Subproblem 2
y + -1.125 = -0.515388203

Simplifying
y + -1.125 = -0.515388203

Reorder the terms:
-1.125 + y = -0.515388203

Solving
-1.125 + y = -0.515388203

Solving for variable 'y'.

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

Add '1.125' to each side of the equation.
-1.125 + 1.125 + y = -0.515388203 + 1.125

Combine like terms: -1.125 + 1.125 = 0.000
0.000 + y = -0.515388203 + 1.125
y = -0.515388203 + 1.125

Combine like terms: -0.515388203 + 1.125 = 0.609611797
y = 0.609611797

Simplifying
y = 0.609611797

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {1.640388203, 0.609611797}
Solution
y = {1.640388203, 0.609611797}