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

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

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

Reorder the terms:
(8 + 4y)(3y + -2) = 2

Reorder the terms:
(8 + 4y)(-2 + 3y) = 2

Multiply (8 + 4y) * (-2 + 3y)
(8(-2 + 3y) + 4y * (-2 + 3y)) = 2
((-2 * 8 + 3y * 8) + 4y * (-2 + 3y)) = 2
((-16 + 24y) + 4y * (-2 + 3y)) = 2
(-16 + 24y + (-2 * 4y + 3y * 4y)) = 2
(-16 + 24y + (-8y + 12y2)) = 2

Combine like terms: 24y + -8y = 16y
(-16 + 16y + 12y2) = 2

Solving
-16 + 16y + 12y2 = 2

Solving for variable 'y'.

Reorder the terms:
-16 + -2 + 16y + 12y2 = 2 + -2

Combine like terms: -16 + -2 = -18
-18 + 16y + 12y2 = 2 + -2

Combine like terms: 2 + -2 = 0
-18 + 16y + 12y2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-9 + 8y + 6y2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-9 + 8y + 6y2)' equal to zero and attempt to solve:

Simplifying
-9 + 8y + 6y2 = 0

Solving
-9 + 8y + 6y2 = 0

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

Divide each side by '6'.
-1.5 + 1.333333333y + y2 = 0

Move the constant term to the right:

Add '1.5' to each side of the equation.
-1.5 + 1.333333333y + 1.5 + y2 = 0 + 1.5

Reorder the terms:
-1.5 + 1.5 + 1.333333333y + y2 = 0 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + 1.333333333y + y2 = 0 + 1.5
1.333333333y + y2 = 0 + 1.5

Combine like terms: 0 + 1.5 = 1.5
1.333333333y + y2 = 1.5

The y term is 1.333333333y.  Take half its coefficient (0.6666666665).
Square it (0.4444444442) and add it to both sides.

Add '0.4444444442' to each side of the equation.
1.333333333y + 0.4444444442 + y2 = 1.5 + 0.4444444442

Reorder the terms:
0.4444444442 + 1.333333333y + y2 = 1.5 + 0.4444444442

Combine like terms: 1.5 + 0.4444444442 = 1.9444444442
0.4444444442 + 1.333333333y + y2 = 1.9444444442

Factor a perfect square on the left side:
(y + 0.6666666665)(y + 0.6666666665) = 1.9444444442

Calculate the square root of the right side: 1.394433377

Break this problem into two subproblems by setting 
(y + 0.6666666665) equal to 1.394433377 and -1.394433377.

Subproblem 1
y + 0.6666666665 = 1.394433377

Simplifying
y + 0.6666666665 = 1.394433377

Reorder the terms:
0.6666666665 + y = 1.394433377

Solving
0.6666666665 + y = 1.394433377

Solving for variable 'y'.

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

Add '-0.6666666665' to each side of the equation.
0.6666666665 + -0.6666666665 + y = 1.394433377 + -0.6666666665

Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000
0.0000000000 + y = 1.394433377 + -0.6666666665
y = 1.394433377 + -0.6666666665

Combine like terms: 1.394433377 + -0.6666666665 = 0.7277667105
y = 0.7277667105

Simplifying
y = 0.7277667105

Subproblem 2
y + 0.6666666665 = -1.394433377

Simplifying
y + 0.6666666665 = -1.394433377

Reorder the terms:
0.6666666665 + y = -1.394433377

Solving
0.6666666665 + y = -1.394433377

Solving for variable 'y'.

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

Add '-0.6666666665' to each side of the equation.
0.6666666665 + -0.6666666665 + y = -1.394433377 + -0.6666666665

Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000
0.0000000000 + y = -1.394433377 + -0.6666666665
y = -1.394433377 + -0.6666666665

Combine like terms: -1.394433377 + -0.6666666665 = -2.0611000435
y = -2.0611000435

Simplifying
y = -2.0611000435

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {0.7277667105, -2.0611000435}
Solution
y = {0.7277667105, -2.0611000435}