3(2y-8)-2y(5-y)=

Solution for 3(2y-8)-2y(5-y)= equation:

Simplifying
3(2y + -8) + -2y(5 + -1y) = 0

Reorder the terms:
3(-8 + 2y) + -2y(5 + -1y) = 0
(-8 * 3 + 2y * 3) + -2y(5 + -1y) = 0
(-24 + 6y) + -2y(5 + -1y) = 0
-24 + 6y + (5 * -2y + -1y * -2y) = 0
-24 + 6y + (-10y + 2y2) = 0

Combine like terms: 6y + -10y = -4y
-24 + -4y + 2y2 = 0

Solving
-24 + -4y + 2y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-12 + -2y + y2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-12 + -2y + y2)' equal to zero and attempt to solve:

Simplifying
-12 + -2y + y2 = 0

Solving
-12 + -2y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '12' to each side of the equation.
-12 + -2y + 12 + y2 = 0 + 12

Reorder the terms:
-12 + 12 + -2y + y2 = 0 + 12

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

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

The y term is -2y.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2y + 1 + y2 = 12 + 1

Reorder the terms:
1 + -2y + y2 = 12 + 1

Combine like terms: 12 + 1 = 13
1 + -2y + y2 = 13

Factor a perfect square on the left side:
(y + -1)(y + -1) = 13

Calculate the square root of the right side: 3.605551275

Break this problem into two subproblems by setting 
(y + -1) equal to 3.605551275 and -3.605551275.

Subproblem 1
y + -1 = 3.605551275

Simplifying
y + -1 = 3.605551275

Reorder the terms:
-1 + y = 3.605551275

Solving
-1 + y = 3.605551275

Solving for variable 'y'.

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

Add '1' to each side of the equation.
-1 + 1 + y = 3.605551275 + 1

Combine like terms: -1 + 1 = 0
0 + y = 3.605551275 + 1
y = 3.605551275 + 1

Combine like terms: 3.605551275 + 1 = 4.605551275
y = 4.605551275

Simplifying
y = 4.605551275

Subproblem 2
y + -1 = -3.605551275

Simplifying
y + -1 = -3.605551275

Reorder the terms:
-1 + y = -3.605551275

Solving
-1 + y = -3.605551275

Solving for variable 'y'.

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

Add '1' to each side of the equation.
-1 + 1 + y = -3.605551275 + 1

Combine like terms: -1 + 1 = 0
0 + y = -3.605551275 + 1
y = -3.605551275 + 1

Combine like terms: -3.605551275 + 1 = -2.605551275
y = -2.605551275

Simplifying
y = -2.605551275

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {4.605551275, -2.605551275}
Solution
y = {4.605551275, -2.605551275}