8y(-y^2+9y-11)-3(2y^3-6y^2-3y)=

Solution for 8y(-y^2+9y-11)-3(2y^3-6y^2-3y)= equation:

Simplifying
8y(-1y2 + 9y + -11) + -3(2y3 + -6y2 + -3y) = 0

Reorder the terms:
8y(-11 + 9y + -1y2) + -3(2y3 + -6y2 + -3y) = 0
(-11 * 8y + 9y * 8y + -1y2 * 8y) + -3(2y3 + -6y2 + -3y) = 0
(-88y + 72y2 + -8y3) + -3(2y3 + -6y2 + -3y) = 0

Reorder the terms:
-88y + 72y2 + -8y3 + -3(-3y + -6y2 + 2y3) = 0
-88y + 72y2 + -8y3 + (-3y * -3 + -6y2 * -3 + 2y3 * -3) = 0
-88y + 72y2 + -8y3 + (9y + 18y2 + -6y3) = 0

Reorder the terms:
-88y + 9y + 72y2 + 18y2 + -8y3 + -6y3 = 0

Combine like terms: -88y + 9y = -79y
-79y + 72y2 + 18y2 + -8y3 + -6y3 = 0

Combine like terms: 72y2 + 18y2 = 90y2
-79y + 90y2 + -8y3 + -6y3 = 0

Combine like terms: -8y3 + -6y3 = -14y3
-79y + 90y2 + -14y3 = 0

Solving
-79y + 90y2 + -14y3 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), 'y'.
y(-79 + 90y + -14y2) = 0

Subproblem 1
Set the factor 'y' equal to zero and attempt to solve:

Simplifying
y = 0

Solving
y = 0

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

Simplifying
y = 0
Subproblem 2
Set the factor '(-79 + 90y + -14y2)' equal to zero and attempt to solve:

Simplifying
-79 + 90y + -14y2 = 0

Solving
-79 + 90y + -14y2 = 0

Begin completing the square.  Divide all terms by
-14 the coefficient of the squared term: 

Divide each side by '-14'.
5.642857143 + -6.428571429y + y2 = 0

Move the constant term to the right:

Add '-5.642857143' to each side of the equation.
5.642857143 + -6.428571429y + -5.642857143 + y2 = 0 + -5.642857143

Reorder the terms:
5.642857143 + -5.642857143 + -6.428571429y + y2 = 0 + -5.642857143

Combine like terms: 5.642857143 + -5.642857143 = 0.000000000
0.000000000 + -6.428571429y + y2 = 0 + -5.642857143
-6.428571429y + y2 = 0 + -5.642857143

Combine like terms: 0 + -5.642857143 = -5.642857143
-6.428571429y + y2 = -5.642857143

The y term is -6.428571429y.  Take half its coefficient (-3.214285715).
Square it (10.33163266) and add it to both sides.

Add '10.33163266' to each side of the equation.
-6.428571429y + 10.33163266 + y2 = -5.642857143 + 10.33163266

Reorder the terms:
10.33163266 + -6.428571429y + y2 = -5.642857143 + 10.33163266

Combine like terms: -5.642857143 + 10.33163266 = 4.688775517
10.33163266 + -6.428571429y + y2 = 4.688775517

Factor a perfect square on the left side:
(y + -3.214285715)(y + -3.214285715) = 4.688775517

Calculate the square root of the right side: 2.165358057

Break this problem into two subproblems by setting 
(y + -3.214285715) equal to 2.165358057 and -2.165358057.

Subproblem 1
y + -3.214285715 = 2.165358057

Simplifying
y + -3.214285715 = 2.165358057

Reorder the terms:
-3.214285715 + y = 2.165358057

Solving
-3.214285715 + y = 2.165358057

Solving for variable 'y'.

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

Add '3.214285715' to each side of the equation.
-3.214285715 + 3.214285715 + y = 2.165358057 + 3.214285715

Combine like terms: -3.214285715 + 3.214285715 = 0.000000000
0.000000000 + y = 2.165358057 + 3.214285715
y = 2.165358057 + 3.214285715

Combine like terms: 2.165358057 + 3.214285715 = 5.379643772
y = 5.379643772

Simplifying
y = 5.379643772

Subproblem 2
y + -3.214285715 = -2.165358057

Simplifying
y + -3.214285715 = -2.165358057

Reorder the terms:
-3.214285715 + y = -2.165358057

Solving
-3.214285715 + y = -2.165358057

Solving for variable 'y'.

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

Add '3.214285715' to each side of the equation.
-3.214285715 + 3.214285715 + y = -2.165358057 + 3.214285715

Combine like terms: -3.214285715 + 3.214285715 = 0.000000000
0.000000000 + y = -2.165358057 + 3.214285715
y = -2.165358057 + 3.214285715

Combine like terms: -2.165358057 + 3.214285715 = 1.048927658
y = 1.048927658

Simplifying
y = 1.048927658

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {5.379643772, 1.048927658}
Solution
y = {0, 5.379643772, 1.048927658}