8y(3y-8)=3(y+1)-2

Solution for 8y(3y-8)=3(y+1)-2 equation:

Simplifying
8y(3y + -8) = 3(y + 1) + -2

Reorder the terms:
8y(-8 + 3y) = 3(y + 1) + -2
(-8 * 8y + 3y * 8y) = 3(y + 1) + -2
(-64y + 24y2) = 3(y + 1) + -2

Reorder the terms:
-64y + 24y2 = 3(1 + y) + -2
-64y + 24y2 = (1 * 3 + y * 3) + -2
-64y + 24y2 = (3 + 3y) + -2

Reorder the terms:
-64y + 24y2 = 3 + -2 + 3y

Combine like terms: 3 + -2 = 1
-64y + 24y2 = 1 + 3y

Solving
-64y + 24y2 = 1 + 3y

Solving for variable 'y'.

Reorder the terms:
-1 + -64y + -3y + 24y2 = 1 + 3y + -1 + -3y

Combine like terms: -64y + -3y = -67y
-1 + -67y + 24y2 = 1 + 3y + -1 + -3y

Reorder the terms:
-1 + -67y + 24y2 = 1 + -1 + 3y + -3y

Combine like terms: 1 + -1 = 0
-1 + -67y + 24y2 = 0 + 3y + -3y
-1 + -67y + 24y2 = 3y + -3y

Combine like terms: 3y + -3y = 0
-1 + -67y + 24y2 = 0

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

Divide each side by '24'.
-0.04166666667 + -2.791666667y + y2 = 0

Move the constant term to the right:

Add '0.04166666667' to each side of the equation.
-0.04166666667 + -2.791666667y + 0.04166666667 + y2 = 0 + 0.04166666667

Reorder the terms:
-0.04166666667 + 0.04166666667 + -2.791666667y + y2 = 0 + 0.04166666667

Combine like terms: -0.04166666667 + 0.04166666667 = 0.00000000000
0.00000000000 + -2.791666667y + y2 = 0 + 0.04166666667
-2.791666667y + y2 = 0 + 0.04166666667

Combine like terms: 0 + 0.04166666667 = 0.04166666667
-2.791666667y + y2 = 0.04166666667

The y term is -2.791666667y.  Take half its coefficient (-1.395833334).
Square it (1.948350696) and add it to both sides.

Add '1.948350696' to each side of the equation.
-2.791666667y + 1.948350696 + y2 = 0.04166666667 + 1.948350696

Reorder the terms:
1.948350696 + -2.791666667y + y2 = 0.04166666667 + 1.948350696

Combine like terms: 0.04166666667 + 1.948350696 = 1.99001736267
1.948350696 + -2.791666667y + y2 = 1.99001736267

Factor a perfect square on the left side:
(y + -1.395833334)(y + -1.395833334) = 1.99001736267

Calculate the square root of the right side: 1.410679752

Break this problem into two subproblems by setting 
(y + -1.395833334) equal to 1.410679752 and -1.410679752.

Subproblem 1
y + -1.395833334 = 1.410679752

Simplifying
y + -1.395833334 = 1.410679752

Reorder the terms:
-1.395833334 + y = 1.410679752

Solving
-1.395833334 + y = 1.410679752

Solving for variable 'y'.

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

Add '1.395833334' to each side of the equation.
-1.395833334 + 1.395833334 + y = 1.410679752 + 1.395833334

Combine like terms: -1.395833334 + 1.395833334 = 0.000000000
0.000000000 + y = 1.410679752 + 1.395833334
y = 1.410679752 + 1.395833334

Combine like terms: 1.410679752 + 1.395833334 = 2.806513086
y = 2.806513086

Simplifying
y = 2.806513086

Subproblem 2
y + -1.395833334 = -1.410679752

Simplifying
y + -1.395833334 = -1.410679752

Reorder the terms:
-1.395833334 + y = -1.410679752

Solving
-1.395833334 + y = -1.410679752

Solving for variable 'y'.

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

Add '1.395833334' to each side of the equation.
-1.395833334 + 1.395833334 + y = -1.410679752 + 1.395833334

Combine like terms: -1.395833334 + 1.395833334 = 0.000000000
0.000000000 + y = -1.410679752 + 1.395833334
y = -1.410679752 + 1.395833334

Combine like terms: -1.410679752 + 1.395833334 = -0.014846418
y = -0.014846418

Simplifying
y = -0.014846418

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {2.806513086, -0.014846418}