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

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

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

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

Reorder the terms for easier multiplication:
6 * 2(1 + y)(3 + -1y) = 7y

Multiply 6 * 2
12(1 + y)(3 + -1y) = 7y

Multiply (1 + y) * (3 + -1y)
12(1(3 + -1y) + y(3 + -1y)) = 7y
12((3 * 1 + -1y * 1) + y(3 + -1y)) = 7y
12((3 + -1y) + y(3 + -1y)) = 7y
12(3 + -1y + (3 * y + -1y * y)) = 7y
12(3 + -1y + (3y + -1y2)) = 7y

Combine like terms: -1y + 3y = 2y
12(3 + 2y + -1y2) = 7y
(3 * 12 + 2y * 12 + -1y2 * 12) = 7y
(36 + 24y + -12y2) = 7y

Solving
36 + 24y + -12y2 = 7y

Solving for variable 'y'.

Reorder the terms:
36 + 24y + -7y + -12y2 = 7y + -7y

Combine like terms: 24y + -7y = 17y
36 + 17y + -12y2 = 7y + -7y

Combine like terms: 7y + -7y = 0
36 + 17y + -12y2 = 0

Begin completing the square.  Divide all terms by
-12 the coefficient of the squared term: 

Divide each side by '-12'.
-3 + -1.416666667y + y2 = 0

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + -1.416666667y + 3 + y2 = 0 + 3

Reorder the terms:
-3 + 3 + -1.416666667y + y2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1.416666667y + y2 = 0 + 3
-1.416666667y + y2 = 0 + 3

Combine like terms: 0 + 3 = 3
-1.416666667y + y2 = 3

The y term is -1.416666667y.  Take half its coefficient (-0.7083333335).
Square it (0.5017361113) and add it to both sides.

Add '0.5017361113' to each side of the equation.
-1.416666667y + 0.5017361113 + y2 = 3 + 0.5017361113

Reorder the terms:
0.5017361113 + -1.416666667y + y2 = 3 + 0.5017361113

Combine like terms: 3 + 0.5017361113 = 3.5017361113
0.5017361113 + -1.416666667y + y2 = 3.5017361113

Factor a perfect square on the left side:
(y + -0.7083333335)(y + -0.7083333335) = 3.5017361113

Calculate the square root of the right side: 1.871292631

Break this problem into two subproblems by setting 
(y + -0.7083333335) equal to 1.871292631 and -1.871292631.

Subproblem 1
y + -0.7083333335 = 1.871292631

Simplifying
y + -0.7083333335 = 1.871292631

Reorder the terms:
-0.7083333335 + y = 1.871292631

Solving
-0.7083333335 + y = 1.871292631

Solving for variable 'y'.

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

Add '0.7083333335' to each side of the equation.
-0.7083333335 + 0.7083333335 + y = 1.871292631 + 0.7083333335

Combine like terms: -0.7083333335 + 0.7083333335 = 0.0000000000
0.0000000000 + y = 1.871292631 + 0.7083333335
y = 1.871292631 + 0.7083333335

Combine like terms: 1.871292631 + 0.7083333335 = 2.5796259645
y = 2.5796259645

Simplifying
y = 2.5796259645

Subproblem 2
y + -0.7083333335 = -1.871292631

Simplifying
y + -0.7083333335 = -1.871292631

Reorder the terms:
-0.7083333335 + y = -1.871292631

Solving
-0.7083333335 + y = -1.871292631

Solving for variable 'y'.

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

Add '0.7083333335' to each side of the equation.
-0.7083333335 + 0.7083333335 + y = -1.871292631 + 0.7083333335

Combine like terms: -0.7083333335 + 0.7083333335 = 0.0000000000
0.0000000000 + y = -1.871292631 + 0.7083333335
y = -1.871292631 + 0.7083333335

Combine like terms: -1.871292631 + 0.7083333335 = -1.1629592975
y = -1.1629592975

Simplifying
y = -1.1629592975

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {2.5796259645, -1.1629592975}