3y(y+2)=5

Solution for 3y(y+2)=5 equation:

Simplifying
3y(y + 2) = 5

Reorder the terms:
3y(2 + y) = 5
(2 * 3y + y * 3y) = 5
(6y + 3y2) = 5

Solving
6y + 3y2 = 5

Solving for variable 'y'.

Reorder the terms:
-5 + 6y + 3y2 = 5 + -5

Combine like terms: 5 + -5 = 0
-5 + 6y + 3y2 = 0

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

Divide each side by '3'.
-1.666666667 + 2y + y2 = 0

Move the constant term to the right:

Add '1.666666667' to each side of the equation.
-1.666666667 + 2y + 1.666666667 + y2 = 0 + 1.666666667

Reorder the terms:
-1.666666667 + 1.666666667 + 2y + y2 = 0 + 1.666666667

Combine like terms: -1.666666667 + 1.666666667 = 0.000000000
0.000000000 + 2y + y2 = 0 + 1.666666667
2y + y2 = 0 + 1.666666667

Combine like terms: 0 + 1.666666667 = 1.666666667
2y + y2 = 1.666666667

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 = 1.666666667 + 1

Reorder the terms:
1 + 2y + y2 = 1.666666667 + 1

Combine like terms: 1.666666667 + 1 = 2.666666667
1 + 2y + y2 = 2.666666667

Factor a perfect square on the left side:
(y + 1)(y + 1) = 2.666666667

Calculate the square root of the right side: 1.632993162

Break this problem into two subproblems by setting 
(y + 1) equal to 1.632993162 and -1.632993162.

Subproblem 1
y + 1 = 1.632993162

Simplifying
y + 1 = 1.632993162

Reorder the terms:
1 + y = 1.632993162

Solving
1 + y = 1.632993162

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 = 1.632993162 + -1

Combine like terms: 1 + -1 = 0
0 + y = 1.632993162 + -1
y = 1.632993162 + -1

Combine like terms: 1.632993162 + -1 = 0.632993162
y = 0.632993162

Simplifying
y = 0.632993162

Subproblem 2
y + 1 = -1.632993162

Simplifying
y + 1 = -1.632993162

Reorder the terms:
1 + y = -1.632993162

Solving
1 + y = -1.632993162

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 = -1.632993162 + -1

Combine like terms: 1 + -1 = 0
0 + y = -1.632993162 + -1
y = -1.632993162 + -1

Combine like terms: -1.632993162 + -1 = -2.632993162
y = -2.632993162

Simplifying
y = -2.632993162

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {0.632993162, -2.632993162}