3y-2y(y+19)=9y-3(9-y)

Solution for 3y-2y(y+19)=9y-3(9-y) equation:

Simplifying
3y + -2y(y + 19) = 9y + -3(9 + -1y)

Reorder the terms:
3y + -2y(19 + y) = 9y + -3(9 + -1y)
3y + (19 * -2y + y * -2y) = 9y + -3(9 + -1y)
3y + (-38y + -2y2) = 9y + -3(9 + -1y)

Combine like terms: 3y + -38y = -35y
-35y + -2y2 = 9y + -3(9 + -1y)
-35y + -2y2 = 9y + (9 * -3 + -1y * -3)
-35y + -2y2 = 9y + (-27 + 3y)

Reorder the terms:
-35y + -2y2 = -27 + 9y + 3y

Combine like terms: 9y + 3y = 12y
-35y + -2y2 = -27 + 12y

Solving
-35y + -2y2 = -27 + 12y

Solving for variable 'y'.

Reorder the terms:
27 + -35y + -12y + -2y2 = -27 + 12y + 27 + -12y

Combine like terms: -35y + -12y = -47y
27 + -47y + -2y2 = -27 + 12y + 27 + -12y

Reorder the terms:
27 + -47y + -2y2 = -27 + 27 + 12y + -12y

Combine like terms: -27 + 27 = 0
27 + -47y + -2y2 = 0 + 12y + -12y
27 + -47y + -2y2 = 12y + -12y

Combine like terms: 12y + -12y = 0
27 + -47y + -2y2 = 0

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

Divide each side by '-2'.
-13.5 + 23.5y + y2 = 0

Move the constant term to the right:

Add '13.5' to each side of the equation.
-13.5 + 23.5y + 13.5 + y2 = 0 + 13.5

Reorder the terms:
-13.5 + 13.5 + 23.5y + y2 = 0 + 13.5

Combine like terms: -13.5 + 13.5 = 0.0
0.0 + 23.5y + y2 = 0 + 13.5
23.5y + y2 = 0 + 13.5

Combine like terms: 0 + 13.5 = 13.5
23.5y + y2 = 13.5

The y term is 23.5y.  Take half its coefficient (11.75).
Square it (138.0625) and add it to both sides.

Add '138.0625' to each side of the equation.
23.5y + 138.0625 + y2 = 13.5 + 138.0625

Reorder the terms:
138.0625 + 23.5y + y2 = 13.5 + 138.0625

Combine like terms: 13.5 + 138.0625 = 151.5625
138.0625 + 23.5y + y2 = 151.5625

Factor a perfect square on the left side:
(y + 11.75)(y + 11.75) = 151.5625

Calculate the square root of the right side: 12.311072252

Break this problem into two subproblems by setting 
(y + 11.75) equal to 12.311072252 and -12.311072252.

Subproblem 1
y + 11.75 = 12.311072252

Simplifying
y + 11.75 = 12.311072252

Reorder the terms:
11.75 + y = 12.311072252

Solving
11.75 + y = 12.311072252

Solving for variable 'y'.

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

Add '-11.75' to each side of the equation.
11.75 + -11.75 + y = 12.311072252 + -11.75

Combine like terms: 11.75 + -11.75 = 0.00
0.00 + y = 12.311072252 + -11.75
y = 12.311072252 + -11.75

Combine like terms: 12.311072252 + -11.75 = 0.561072252
y = 0.561072252

Simplifying
y = 0.561072252

Subproblem 2
y + 11.75 = -12.311072252

Simplifying
y + 11.75 = -12.311072252

Reorder the terms:
11.75 + y = -12.311072252

Solving
11.75 + y = -12.311072252

Solving for variable 'y'.

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

Add '-11.75' to each side of the equation.
11.75 + -11.75 + y = -12.311072252 + -11.75

Combine like terms: 11.75 + -11.75 = 0.00
0.00 + y = -12.311072252 + -11.75
y = -12.311072252 + -11.75

Combine like terms: -12.311072252 + -11.75 = -24.061072252
y = -24.061072252

Simplifying
y = -24.061072252

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {0.561072252, -24.061072252}