27=(3+y)(3+y)

Solution for 27=(3+y)(3+y) equation:

Simplifying
27 = (3 + y)(3 + y)

Multiply (3 + y) * (3 + y)
27 = (3(3 + y) + y(3 + y))
27 = ((3 * 3 + y * 3) + y(3 + y))
27 = ((9 + 3y) + y(3 + y))
27 = (9 + 3y + (3 * y + y * y))
27 = (9 + 3y + (3y + y2))

Combine like terms: 3y + 3y = 6y
27 = (9 + 6y + y2)

Solving
27 = 9 + 6y + y2

Solving for variable 'y'.

Combine like terms: 27 + -9 = 18
18 + -6y + -1y2 = 9 + 6y + y2 + -9 + -6y + -1y2

Reorder the terms:
18 + -6y + -1y2 = 9 + -9 + 6y + -6y + y2 + -1y2

Combine like terms: 9 + -9 = 0
18 + -6y + -1y2 = 0 + 6y + -6y + y2 + -1y2
18 + -6y + -1y2 = 6y + -6y + y2 + -1y2

Combine like terms: 6y + -6y = 0
18 + -6y + -1y2 = 0 + y2 + -1y2
18 + -6y + -1y2 = y2 + -1y2

Combine like terms: y2 + -1y2 = 0
18 + -6y + -1y2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-18 + 6y + y2 = 0

Move the constant term to the right:

Add '18' to each side of the equation.
-18 + 6y + 18 + y2 = 0 + 18

Reorder the terms:
-18 + 18 + 6y + y2 = 0 + 18

Combine like terms: -18 + 18 = 0
0 + 6y + y2 = 0 + 18
6y + y2 = 0 + 18

Combine like terms: 0 + 18 = 18
6y + y2 = 18

The y term is 6y.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6y + 9 + y2 = 18 + 9

Reorder the terms:
9 + 6y + y2 = 18 + 9

Combine like terms: 18 + 9 = 27
9 + 6y + y2 = 27

Factor a perfect square on the left side:
(y + 3)(y + 3) = 27

Calculate the square root of the right side: 5.196152423

Break this problem into two subproblems by setting 
(y + 3) equal to 5.196152423 and -5.196152423.

Subproblem 1
y + 3 = 5.196152423

Simplifying
y + 3 = 5.196152423

Reorder the terms:
3 + y = 5.196152423

Solving
3 + y = 5.196152423

Solving for variable 'y'.

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

Add '-3' to each side of the equation.
3 + -3 + y = 5.196152423 + -3

Combine like terms: 3 + -3 = 0
0 + y = 5.196152423 + -3
y = 5.196152423 + -3

Combine like terms: 5.196152423 + -3 = 2.196152423
y = 2.196152423

Simplifying
y = 2.196152423

Subproblem 2
y + 3 = -5.196152423

Simplifying
y + 3 = -5.196152423

Reorder the terms:
3 + y = -5.196152423

Solving
3 + y = -5.196152423

Solving for variable 'y'.

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

Add '-3' to each side of the equation.
3 + -3 + y = -5.196152423 + -3

Combine like terms: 3 + -3 = 0
0 + y = -5.196152423 + -3
y = -5.196152423 + -3

Combine like terms: -5.196152423 + -3 = -8.196152423
y = -8.196152423

Simplifying
y = -8.196152423

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {2.196152423, -8.196152423}