3(y-1)y-2y+2(y-1)=

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Solution for 3(y-1)y-2y+2(y-1)= equation: 


Simplifying
3(y + -1) * y + -2y + 2(y + -1) = 0

Reorder the terms:
3(-1 + y) * y + -2y + 2(y + -1) = 0

Reorder the terms for easier multiplication:
3y(-1 + y) + -2y + 2(y + -1) = 0
(-1 * 3y + y * 3y) + -2y + 2(y + -1) = 0
(-3y + 3y2) + -2y + 2(y + -1) = 0

Reorder the terms:
-3y + 3y2 + -2y + 2(-1 + y) = 0
-3y + 3y2 + -2y + (-1 * 2 + y * 2) = 0
-3y + 3y2 + -2y + (-2 + 2y) = 0

Reorder the terms:
-2 + -3y + -2y + 2y + 3y2 = 0

Combine like terms: -3y + -2y = -5y
-2 + -5y + 2y + 3y2 = 0

Combine like terms: -5y + 2y = -3y
-2 + -3y + 3y2 = 0

Solving
-2 + -3y + 3y2 = 0

Solving for variable 'y'.

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

Divide each side by '3'.
-0.6666666667 + -1y + y2 = 0

Move the constant term to the right:

Add '0.6666666667' to each side of the equation.
-0.6666666667 + -1y + 0.6666666667 + y2 = 0 + 0.6666666667

Reorder the terms:
-0.6666666667 + 0.6666666667 + -1y + y2 = 0 + 0.6666666667

Combine like terms: -0.6666666667 + 0.6666666667 = 0.0000000000
0.0000000000 + -1y + y2 = 0 + 0.6666666667
-1y + y2 = 0 + 0.6666666667

Combine like terms: 0 + 0.6666666667 = 0.6666666667
-1y + y2 = 0.6666666667

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 = 0.6666666667 + 0.25

Reorder the terms:
0.25 + -1y + y2 = 0.6666666667 + 0.25

Combine like terms: 0.6666666667 + 0.25 = 0.9166666667
0.25 + -1y + y2 = 0.9166666667

Factor a perfect square on the left side:
(y + -0.5)(y + -0.5) = 0.9166666667

Calculate the square root of the right side: 0.957427108

Break this problem into two subproblems by setting 
(y + -0.5) equal to 0.957427108 and -0.957427108.


Subproblem 1
y + -0.5 = 0.957427108

Simplifying
y + -0.5 = 0.957427108

Reorder the terms:
-0.5 + y = 0.957427108

Solving
-0.5 + y = 0.957427108

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 = 0.957427108 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + y = 0.957427108 + 0.5
y = 0.957427108 + 0.5

Combine like terms: 0.957427108 + 0.5 = 1.457427108
y = 1.457427108

Simplifying
y = 1.457427108


Subproblem 2
y + -0.5 = -0.957427108

Simplifying
y + -0.5 = -0.957427108

Reorder the terms:
-0.5 + y = -0.957427108

Solving
-0.5 + y = -0.957427108

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 = -0.957427108 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + y = -0.957427108 + 0.5
y = -0.957427108 + 0.5

Combine like terms: -0.957427108 + 0.5 = -0.457427108
y = -0.457427108

Simplifying
y = -0.457427108


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {1.457427108, -0.457427108}

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