(3-3y^2)-2y(3-3y)+3y^2=27

Solution for (3-3y^2)-2y(3-3y)+3y^2=27 equation:

Simplifying
(3 + -3y2) + -2y(3 + -3y) + 3y2 = 27

Remove parenthesis around (3 + -3y2)
3 + -3y2 + -2y(3 + -3y) + 3y2 = 27
3 + -3y2 + (3 * -2y + -3y * -2y) + 3y2 = 27
3 + -3y2 + (-6y + 6y2) + 3y2 = 27

Reorder the terms:
3 + -6y + -3y2 + 6y2 + 3y2 = 27

Combine like terms: -3y2 + 6y2 = 3y2
3 + -6y + 3y2 + 3y2 = 27

Combine like terms: 3y2 + 3y2 = 6y2
3 + -6y + 6y2 = 27

Solving
3 + -6y + 6y2 = 27

Solving for variable 'y'.

Reorder the terms:
3 + -27 + -6y + 6y2 = 27 + -27

Combine like terms: 3 + -27 = -24
-24 + -6y + 6y2 = 27 + -27

Combine like terms: 27 + -27 = 0
-24 + -6y + 6y2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(-4 + -1y + y2) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(-4 + -1y + y2)' equal to zero and attempt to solve:

Simplifying
-4 + -1y + y2 = 0

Solving
-4 + -1y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + -1y + 4 + y2 = 0 + 4

Reorder the terms:
-4 + 4 + -1y + y2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1y + y2 = 0 + 4
-1y + y2 = 0 + 4

Combine like terms: 0 + 4 = 4
-1y + y2 = 4

The y term is -1y.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1y + 0.25 + y2 = 4 + 0.25

Reorder the terms:
0.25 + -1y + y2 = 4 + 0.25

Combine like terms: 4 + 0.25 = 4.25
0.25 + -1y + y2 = 4.25

Factor a perfect square on the left side:
(y + -0.5)(y + -0.5) = 4.25

Calculate the square root of the right side: 2.061552813

Break this problem into two subproblems by setting 
(y + -0.5) equal to 2.061552813 and -2.061552813.

Subproblem 1
y + -0.5 = 2.061552813

Simplifying
y + -0.5 = 2.061552813

Reorder the terms:
-0.5 + y = 2.061552813

Solving
-0.5 + y = 2.061552813

Solving for variable 'y'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + y = 2.061552813 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + y = 2.061552813 + 0.5
y = 2.061552813 + 0.5

Combine like terms: 2.061552813 + 0.5 = 2.561552813
y = 2.561552813

Simplifying
y = 2.561552813

Subproblem 2
y + -0.5 = -2.061552813

Simplifying
y + -0.5 = -2.061552813

Reorder the terms:
-0.5 + y = -2.061552813

Solving
-0.5 + y = -2.061552813

Solving for variable 'y'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + y = -2.061552813 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + y = -2.061552813 + 0.5
y = -2.061552813 + 0.5

Combine like terms: -2.061552813 + 0.5 = -1.561552813
y = -1.561552813

Simplifying
y = -1.561552813

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {2.561552813, -1.561552813}
Solution
y = {2.561552813, -1.561552813}