54=2y^2-2y

Solution for 54=2y^2-2y equation:

Simplifying
54 = 2y2 + -2y

Reorder the terms:
54 = -2y + 2y2

Solving
54 = -2y + 2y2

Solving for variable 'y'.

Reorder the terms:
54 + 2y + -2y2 = -2y + 2y + 2y2 + -2y2

Combine like terms: -2y + 2y = 0
54 + 2y + -2y2 = 0 + 2y2 + -2y2
54 + 2y + -2y2 = 2y2 + -2y2

Combine like terms: 2y2 + -2y2 = 0
54 + 2y + -2y2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(27 + y + -1y2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(27 + y + -1y2)' equal to zero and attempt to solve:

Simplifying
27 + y + -1y2 = 0

Solving
27 + y + -1y2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-27 + -1y + y2 = 0

Move the constant term to the right:

Add '27' to each side of the equation.
-27 + -1y + 27 + y2 = 0 + 27

Reorder the terms:
-27 + 27 + -1y + y2 = 0 + 27

Combine like terms: -27 + 27 = 0
0 + -1y + y2 = 0 + 27
-1y + y2 = 0 + 27

Combine like terms: 0 + 27 = 27
-1y + y2 = 27

The y term is y.  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 = 27 + 0.25

Reorder the terms:
0.25 + -1y + y2 = 27 + 0.25

Combine like terms: 27 + 0.25 = 27.25
0.25 + -1y + y2 = 27.25

Factor a perfect square on the left side:
(y + 0.5)(y + 0.5) = 27.25

Calculate the square root of the right side: 5.220153254

Break this problem into two subproblems by setting 
(y + 0.5) equal to 5.220153254 and -5.220153254.

Subproblem 1
y + 0.5 = 5.220153254

Simplifying
y + 0.5 = 5.220153254

Reorder the terms:
0.5 + y = 5.220153254

Solving
0.5 + y = 5.220153254

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 = 5.220153254 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + y = 5.220153254 + -0.5
y = 5.220153254 + -0.5

Combine like terms: 5.220153254 + -0.5 = 4.720153254
y = 4.720153254

Simplifying
y = 4.720153254

Subproblem 2
y + 0.5 = -5.220153254

Simplifying
y + 0.5 = -5.220153254

Reorder the terms:
0.5 + y = -5.220153254

Solving
0.5 + y = -5.220153254

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 = -5.220153254 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + y = -5.220153254 + -0.5
y = -5.220153254 + -0.5

Combine like terms: -5.220153254 + -0.5 = -5.720153254
y = -5.720153254

Simplifying
y = -5.720153254

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {4.720153254, -5.720153254}
Solution
y = {4.720153254, -5.720153254}