7y+2y(y-6)=3(y-1)-2

Solution for 7y+2y(y-6)=3(y-1)-2 equation:

Simplifying
7y + 2y(y + -6) = 3(y + -1) + -2

Reorder the terms:
7y + 2y(-6 + y) = 3(y + -1) + -2
7y + (-6 * 2y + y * 2y) = 3(y + -1) + -2
7y + (-12y + 2y2) = 3(y + -1) + -2

Combine like terms: 7y + -12y = -5y
-5y + 2y2 = 3(y + -1) + -2

Reorder the terms:
-5y + 2y2 = 3(-1 + y) + -2
-5y + 2y2 = (-1 * 3 + y * 3) + -2
-5y + 2y2 = (-3 + 3y) + -2

Reorder the terms:
-5y + 2y2 = -3 + -2 + 3y

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

Solving
-5y + 2y2 = -5 + 3y

Solving for variable 'y'.

Reorder the terms:
5 + -5y + -3y + 2y2 = -5 + 3y + 5 + -3y

Combine like terms: -5y + -3y = -8y
5 + -8y + 2y2 = -5 + 3y + 5 + -3y

Reorder the terms:
5 + -8y + 2y2 = -5 + 5 + 3y + -3y

Combine like terms: -5 + 5 = 0
5 + -8y + 2y2 = 0 + 3y + -3y
5 + -8y + 2y2 = 3y + -3y

Combine like terms: 3y + -3y = 0
5 + -8y + 2y2 = 0

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

Divide each side by '2'.
2.5 + -4y + y2 = 0

Move the constant term to the right:

Add '-2.5' to each side of the equation.
2.5 + -4y + -2.5 + y2 = 0 + -2.5

Reorder the terms:
2.5 + -2.5 + -4y + y2 = 0 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + -4y + y2 = 0 + -2.5
-4y + y2 = 0 + -2.5

Combine like terms: 0 + -2.5 = -2.5
-4y + y2 = -2.5

The y term is -4y.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4y + 4 + y2 = -2.5 + 4

Reorder the terms:
4 + -4y + y2 = -2.5 + 4

Combine like terms: -2.5 + 4 = 1.5
4 + -4y + y2 = 1.5

Factor a perfect square on the left side:
(y + -2)(y + -2) = 1.5

Calculate the square root of the right side: 1.224744871

Break this problem into two subproblems by setting 
(y + -2) equal to 1.224744871 and -1.224744871.

Subproblem 1
y + -2 = 1.224744871

Simplifying
y + -2 = 1.224744871

Reorder the terms:
-2 + y = 1.224744871

Solving
-2 + y = 1.224744871

Solving for variable 'y'.

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

Add '2' to each side of the equation.
-2 + 2 + y = 1.224744871 + 2

Combine like terms: -2 + 2 = 0
0 + y = 1.224744871 + 2
y = 1.224744871 + 2

Combine like terms: 1.224744871 + 2 = 3.224744871
y = 3.224744871

Simplifying
y = 3.224744871

Subproblem 2
y + -2 = -1.224744871

Simplifying
y + -2 = -1.224744871

Reorder the terms:
-2 + y = -1.224744871

Solving
-2 + y = -1.224744871

Solving for variable 'y'.

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

Add '2' to each side of the equation.
-2 + 2 + y = -1.224744871 + 2

Combine like terms: -2 + 2 = 0
0 + y = -1.224744871 + 2
y = -1.224744871 + 2

Combine like terms: -1.224744871 + 2 = 0.775255129
y = 0.775255129

Simplifying
y = 0.775255129

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {3.224744871, 0.775255129}