2y(y-1)+4y=3(y-1)+7

Solution for 2y(y-1)+4y=3(y-1)+7 equation:

Simplifying
2y(y + -1) + 4y = 3(y + -1) + 7

Reorder the terms:
2y(-1 + y) + 4y = 3(y + -1) + 7
(-1 * 2y + y * 2y) + 4y = 3(y + -1) + 7
(-2y + 2y2) + 4y = 3(y + -1) + 7

Reorder the terms:
-2y + 4y + 2y2 = 3(y + -1) + 7

Combine like terms: -2y + 4y = 2y
2y + 2y2 = 3(y + -1) + 7

Reorder the terms:
2y + 2y2 = 3(-1 + y) + 7
2y + 2y2 = (-1 * 3 + y * 3) + 7
2y + 2y2 = (-3 + 3y) + 7

Reorder the terms:
2y + 2y2 = -3 + 7 + 3y

Combine like terms: -3 + 7 = 4
2y + 2y2 = 4 + 3y

Solving
2y + 2y2 = 4 + 3y

Solving for variable 'y'.

Reorder the terms:
-4 + 2y + -3y + 2y2 = 4 + 3y + -4 + -3y

Combine like terms: 2y + -3y = -1y
-4 + -1y + 2y2 = 4 + 3y + -4 + -3y

Reorder the terms:
-4 + -1y + 2y2 = 4 + -4 + 3y + -3y

Combine like terms: 4 + -4 = 0
-4 + -1y + 2y2 = 0 + 3y + -3y
-4 + -1y + 2y2 = 3y + -3y

Combine like terms: 3y + -3y = 0
-4 + -1y + 2y2 = 0

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

Divide each side by '2'.
-2 + -0.5y + y2 = 0

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + -0.5y + 2 + y2 = 0 + 2

Reorder the terms:
-2 + 2 + -0.5y + y2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -0.5y + y2 = 0 + 2
-0.5y + y2 = 0 + 2

Combine like terms: 0 + 2 = 2
-0.5y + y2 = 2

The y term is -0.5y.  Take half its coefficient (-0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
-0.5y + 0.0625 + y2 = 2 + 0.0625

Reorder the terms:
0.0625 + -0.5y + y2 = 2 + 0.0625

Combine like terms: 2 + 0.0625 = 2.0625
0.0625 + -0.5y + y2 = 2.0625

Factor a perfect square on the left side:
(y + -0.25)(y + -0.25) = 2.0625

Calculate the square root of the right side: 1.436140662

Break this problem into two subproblems by setting 
(y + -0.25) equal to 1.436140662 and -1.436140662.

Subproblem 1
y + -0.25 = 1.436140662

Simplifying
y + -0.25 = 1.436140662

Reorder the terms:
-0.25 + y = 1.436140662

Solving
-0.25 + y = 1.436140662

Solving for variable 'y'.

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

Add '0.25' to each side of the equation.
-0.25 + 0.25 + y = 1.436140662 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + y = 1.436140662 + 0.25
y = 1.436140662 + 0.25

Combine like terms: 1.436140662 + 0.25 = 1.686140662
y = 1.686140662

Simplifying
y = 1.686140662

Subproblem 2
y + -0.25 = -1.436140662

Simplifying
y + -0.25 = -1.436140662

Reorder the terms:
-0.25 + y = -1.436140662

Solving
-0.25 + y = -1.436140662

Solving for variable 'y'.

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

Add '0.25' to each side of the equation.
-0.25 + 0.25 + y = -1.436140662 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + y = -1.436140662 + 0.25
y = -1.436140662 + 0.25

Combine like terms: -1.436140662 + 0.25 = -1.186140662
y = -1.186140662

Simplifying
y = -1.186140662

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {1.686140662, -1.186140662}