2(y+2)y=3

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

Simplifying
2(y + 2) * y = 3

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

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

Solving
4y + 2y2 = 3

Solving for variable 'y'.

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

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

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

Divide each side by '2'.
-1.5 + 2y + y2 = 0

Move the constant term to the right:

Add '1.5' to each side of the equation.
-1.5 + 2y + 1.5 + y2 = 0 + 1.5

Reorder the terms:
-1.5 + 1.5 + 2y + y2 = 0 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + 2y + y2 = 0 + 1.5
2y + y2 = 0 + 1.5

Combine like terms: 0 + 1.5 = 1.5
2y + y2 = 1.5

The y term is 2y.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2y + 1 + y2 = 1.5 + 1

Reorder the terms:
1 + 2y + y2 = 1.5 + 1

Combine like terms: 1.5 + 1 = 2.5
1 + 2y + y2 = 2.5

Factor a perfect square on the left side:
(y + 1)(y + 1) = 2.5

Calculate the square root of the right side: 1.58113883

Break this problem into two subproblems by setting 
(y + 1) equal to 1.58113883 and -1.58113883.

Subproblem 1
y + 1 = 1.58113883

Simplifying
y + 1 = 1.58113883

Reorder the terms:
1 + y = 1.58113883

Solving
1 + y = 1.58113883

Solving for variable 'y'.

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

Add '-1' to each side of the equation.
1 + -1 + y = 1.58113883 + -1

Combine like terms: 1 + -1 = 0
0 + y = 1.58113883 + -1
y = 1.58113883 + -1

Combine like terms: 1.58113883 + -1 = 0.58113883
y = 0.58113883

Simplifying
y = 0.58113883

Subproblem 2
y + 1 = -1.58113883

Simplifying
y + 1 = -1.58113883

Reorder the terms:
1 + y = -1.58113883

Solving
1 + y = -1.58113883

Solving for variable 'y'.

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

Add '-1' to each side of the equation.
1 + -1 + y = -1.58113883 + -1

Combine like terms: 1 + -1 = 0
0 + y = -1.58113883 + -1
y = -1.58113883 + -1

Combine like terms: -1.58113883 + -1 = -2.58113883
y = -2.58113883

Simplifying
y = -2.58113883

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {0.58113883, -2.58113883}