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

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

Simplifying
2(y + 2) * y = 19 + -2(y + 3)

Reorder the terms:
2(2 + y) * y = 19 + -2(y + 3)

Reorder the terms for easier multiplication:
2y(2 + y) = 19 + -2(y + 3)
(2 * 2y + y * 2y) = 19 + -2(y + 3)
(4y + 2y2) = 19 + -2(y + 3)

Reorder the terms:
4y + 2y2 = 19 + -2(3 + y)
4y + 2y2 = 19 + (3 * -2 + y * -2)
4y + 2y2 = 19 + (-6 + -2y)

Combine like terms: 19 + -6 = 13
4y + 2y2 = 13 + -2y

Solving
4y + 2y2 = 13 + -2y

Solving for variable 'y'.

Reorder the terms:
-13 + 4y + 2y + 2y2 = 13 + -2y + -13 + 2y

Combine like terms: 4y + 2y = 6y
-13 + 6y + 2y2 = 13 + -2y + -13 + 2y

Reorder the terms:
-13 + 6y + 2y2 = 13 + -13 + -2y + 2y

Combine like terms: 13 + -13 = 0
-13 + 6y + 2y2 = 0 + -2y + 2y
-13 + 6y + 2y2 = -2y + 2y

Combine like terms: -2y + 2y = 0
-13 + 6y + 2y2 = 0

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

Divide each side by '2'.
-6.5 + 3y + y2 = 0

Move the constant term to the right:

Add '6.5' to each side of the equation.
-6.5 + 3y + 6.5 + y2 = 0 + 6.5

Reorder the terms:
-6.5 + 6.5 + 3y + y2 = 0 + 6.5

Combine like terms: -6.5 + 6.5 = 0.0
0.0 + 3y + y2 = 0 + 6.5
3y + y2 = 0 + 6.5

Combine like terms: 0 + 6.5 = 6.5
3y + y2 = 6.5

The y term is 3y.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3y + 2.25 + y2 = 6.5 + 2.25

Reorder the terms:
2.25 + 3y + y2 = 6.5 + 2.25

Combine like terms: 6.5 + 2.25 = 8.75
2.25 + 3y + y2 = 8.75

Factor a perfect square on the left side:
(y + 1.5)(y + 1.5) = 8.75

Calculate the square root of the right side: 2.958039892

Break this problem into two subproblems by setting 
(y + 1.5) equal to 2.958039892 and -2.958039892.

Subproblem 1
y + 1.5 = 2.958039892

Simplifying
y + 1.5 = 2.958039892

Reorder the terms:
1.5 + y = 2.958039892

Solving
1.5 + y = 2.958039892

Solving for variable 'y'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + y = 2.958039892 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + y = 2.958039892 + -1.5
y = 2.958039892 + -1.5

Combine like terms: 2.958039892 + -1.5 = 1.458039892
y = 1.458039892

Simplifying
y = 1.458039892

Subproblem 2
y + 1.5 = -2.958039892

Simplifying
y + 1.5 = -2.958039892

Reorder the terms:
1.5 + y = -2.958039892

Solving
1.5 + y = -2.958039892

Solving for variable 'y'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + y = -2.958039892 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + y = -2.958039892 + -1.5
y = -2.958039892 + -1.5

Combine like terms: -2.958039892 + -1.5 = -4.458039892
y = -4.458039892

Simplifying
y = -4.458039892

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {1.458039892, -4.458039892}