3(2y-2)y=5

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

Simplifying
3(2y + -2) * y = 5

Reorder the terms:
3(-2 + 2y) * y = 5

Reorder the terms for easier multiplication:
3y(-2 + 2y) = 5
(-2 * 3y + 2y * 3y) = 5
(-6y + 6y2) = 5

Solving
-6y + 6y2 = 5

Solving for variable 'y'.

Reorder the terms:
-5 + -6y + 6y2 = 5 + -5

Combine like terms: 5 + -5 = 0
-5 + -6y + 6y2 = 0

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

Divide each side by '6'.
-0.8333333333 + -1y + y2 = 0

Move the constant term to the right:

Add '0.8333333333' to each side of the equation.
-0.8333333333 + -1y + 0.8333333333 + y2 = 0 + 0.8333333333

Reorder the terms:
-0.8333333333 + 0.8333333333 + -1y + y2 = 0 + 0.8333333333

Combine like terms: -0.8333333333 + 0.8333333333 = 0.0000000000
0.0000000000 + -1y + y2 = 0 + 0.8333333333
-1y + y2 = 0 + 0.8333333333

Combine like terms: 0 + 0.8333333333 = 0.8333333333
-1y + y2 = 0.8333333333

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 = 0.8333333333 + 0.25

Reorder the terms:
0.25 + -1y + y2 = 0.8333333333 + 0.25

Combine like terms: 0.8333333333 + 0.25 = 1.0833333333
0.25 + -1y + y2 = 1.0833333333

Factor a perfect square on the left side:
(y + -0.5)(y + -0.5) = 1.0833333333

Calculate the square root of the right side: 1.040833

Break this problem into two subproblems by setting 
(y + -0.5) equal to 1.040833 and -1.040833.

Subproblem 1
y + -0.5 = 1.040833

Simplifying
y + -0.5 = 1.040833

Reorder the terms:
-0.5 + y = 1.040833

Solving
-0.5 + y = 1.040833

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 = 1.040833 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + y = 1.040833 + 0.5
y = 1.040833 + 0.5

Combine like terms: 1.040833 + 0.5 = 1.540833
y = 1.540833

Simplifying
y = 1.540833

Subproblem 2
y + -0.5 = -1.040833

Simplifying
y + -0.5 = -1.040833

Reorder the terms:
-0.5 + y = -1.040833

Solving
-0.5 + y = -1.040833

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 = -1.040833 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + y = -1.040833 + 0.5
y = -1.040833 + 0.5

Combine like terms: -1.040833 + 0.5 = -0.540833
y = -0.540833

Simplifying
y = -0.540833

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {1.540833, -0.540833}