3(2.5y+8)*2y=31

Solution for 3(2.5y+8)*2y=31 equation:

Simplifying
3(2.5y + 8) * 2y = 31

Reorder the terms:
3(8 + 2.5y) * 2y = 31

Reorder the terms for easier multiplication:
3 * 2y(8 + 2.5y) = 31

Multiply 3 * 2
6y(8 + 2.5y) = 31
(8 * 6y + 2.5y * 6y) = 31
(48y + 15y2) = 31

Solving
48y + 15y2 = 31

Solving for variable 'y'.

Reorder the terms:
-31 + 48y + 15y2 = 31 + -31

Combine like terms: 31 + -31 = 0
-31 + 48y + 15y2 = 0

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

Divide each side by '15'.
-2.066666667 + 3.2y + y2 = 0

Move the constant term to the right:

Add '2.066666667' to each side of the equation.
-2.066666667 + 3.2y + 2.066666667 + y2 = 0 + 2.066666667

Reorder the terms:
-2.066666667 + 2.066666667 + 3.2y + y2 = 0 + 2.066666667

Combine like terms: -2.066666667 + 2.066666667 = 0.000000000
0.000000000 + 3.2y + y2 = 0 + 2.066666667
3.2y + y2 = 0 + 2.066666667

Combine like terms: 0 + 2.066666667 = 2.066666667
3.2y + y2 = 2.066666667

The y term is 3.2y.  Take half its coefficient (1.6).
Square it (2.56) and add it to both sides.

Add '2.56' to each side of the equation.
3.2y + 2.56 + y2 = 2.066666667 + 2.56

Reorder the terms:
2.56 + 3.2y + y2 = 2.066666667 + 2.56

Combine like terms: 2.066666667 + 2.56 = 4.626666667
2.56 + 3.2y + y2 = 4.626666667

Factor a perfect square on the left side:
(y + 1.6)(y + 1.6) = 4.626666667

Calculate the square root of the right side: 2.150968774

Break this problem into two subproblems by setting 
(y + 1.6) equal to 2.150968774 and -2.150968774.

Subproblem 1
y + 1.6 = 2.150968774

Simplifying
y + 1.6 = 2.150968774

Reorder the terms:
1.6 + y = 2.150968774

Solving
1.6 + y = 2.150968774

Solving for variable 'y'.

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

Add '-1.6' to each side of the equation.
1.6 + -1.6 + y = 2.150968774 + -1.6

Combine like terms: 1.6 + -1.6 = 0.0
0.0 + y = 2.150968774 + -1.6
y = 2.150968774 + -1.6

Combine like terms: 2.150968774 + -1.6 = 0.550968774
y = 0.550968774

Simplifying
y = 0.550968774

Subproblem 2
y + 1.6 = -2.150968774

Simplifying
y + 1.6 = -2.150968774

Reorder the terms:
1.6 + y = -2.150968774

Solving
1.6 + y = -2.150968774

Solving for variable 'y'.

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

Add '-1.6' to each side of the equation.
1.6 + -1.6 + y = -2.150968774 + -1.6

Combine like terms: 1.6 + -1.6 = 0.0
0.0 + y = -2.150968774 + -1.6
y = -2.150968774 + -1.6

Combine like terms: -2.150968774 + -1.6 = -3.750968774
y = -3.750968774

Simplifying
y = -3.750968774

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {0.550968774, -3.750968774}