2(4+-1.5y)3y=8

Solution for 2(4+-1.5y)3y=8 equation:

Simplifying
2(4 + -1.5y) * 3y = 8

Reorder the terms for easier multiplication:
2 * 3y(4 + -1.5y) = 8

Multiply 2 * 3
6y(4 + -1.5y) = 8
(4 * 6y + -1.5y * 6y) = 8
(24y + -9y2) = 8

Solving
24y + -9y2 = 8

Solving for variable 'y'.

Reorder the terms:
-8 + 24y + -9y2 = 8 + -8

Combine like terms: 8 + -8 = 0
-8 + 24y + -9y2 = 0

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

Divide each side by '-9'.
0.8888888889 + -2.666666667y + y2 = 0

Move the constant term to the right:

Add '-0.8888888889' to each side of the equation.
0.8888888889 + -2.666666667y + -0.8888888889 + y2 = 0 + -0.8888888889

Reorder the terms:
0.8888888889 + -0.8888888889 + -2.666666667y + y2 = 0 + -0.8888888889

Combine like terms: 0.8888888889 + -0.8888888889 = 0.0000000000
0.0000000000 + -2.666666667y + y2 = 0 + -0.8888888889
-2.666666667y + y2 = 0 + -0.8888888889

Combine like terms: 0 + -0.8888888889 = -0.8888888889
-2.666666667y + y2 = -0.8888888889

The y term is -2.666666667y.  Take half its coefficient (-1.333333334).
Square it (1.777777780) and add it to both sides.

Add '1.777777780' to each side of the equation.
-2.666666667y + 1.777777780 + y2 = -0.8888888889 + 1.777777780

Reorder the terms:
1.777777780 + -2.666666667y + y2 = -0.8888888889 + 1.777777780

Combine like terms: -0.8888888889 + 1.777777780 = 0.8888888911
1.777777780 + -2.666666667y + y2 = 0.8888888911

Factor a perfect square on the left side:
(y + -1.333333334)(y + -1.333333334) = 0.8888888911

Calculate the square root of the right side: 0.942809043

Break this problem into two subproblems by setting 
(y + -1.333333334) equal to 0.942809043 and -0.942809043.

Subproblem 1
y + -1.333333334 = 0.942809043

Simplifying
y + -1.333333334 = 0.942809043

Reorder the terms:
-1.333333334 + y = 0.942809043

Solving
-1.333333334 + y = 0.942809043

Solving for variable 'y'.

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

Add '1.333333334' to each side of the equation.
-1.333333334 + 1.333333334 + y = 0.942809043 + 1.333333334

Combine like terms: -1.333333334 + 1.333333334 = 0.000000000
0.000000000 + y = 0.942809043 + 1.333333334
y = 0.942809043 + 1.333333334

Combine like terms: 0.942809043 + 1.333333334 = 2.276142377
y = 2.276142377

Simplifying
y = 2.276142377

Subproblem 2
y + -1.333333334 = -0.942809043

Simplifying
y + -1.333333334 = -0.942809043

Reorder the terms:
-1.333333334 + y = -0.942809043

Solving
-1.333333334 + y = -0.942809043

Solving for variable 'y'.

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

Add '1.333333334' to each side of the equation.
-1.333333334 + 1.333333334 + y = -0.942809043 + 1.333333334

Combine like terms: -1.333333334 + 1.333333334 = 0.000000000
0.000000000 + y = -0.942809043 + 1.333333334
y = -0.942809043 + 1.333333334

Combine like terms: -0.942809043 + 1.333333334 = 0.390524291
y = 0.390524291

Simplifying
y = 0.390524291

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {2.276142377, 0.390524291}