135=(2y+3)(2y+3)

Solution for 135=(2y+3)(2y+3) equation:

Simplifying
135 = (2y + 3)(2y + 3)

Reorder the terms:
135 = (3 + 2y)(2y + 3)

Reorder the terms:
135 = (3 + 2y)(3 + 2y)

Multiply (3 + 2y) * (3 + 2y)
135 = (3(3 + 2y) + 2y * (3 + 2y))
135 = ((3 * 3 + 2y * 3) + 2y * (3 + 2y))
135 = ((9 + 6y) + 2y * (3 + 2y))
135 = (9 + 6y + (3 * 2y + 2y * 2y))
135 = (9 + 6y + (6y + 4y2))

Combine like terms: 6y + 6y = 12y
135 = (9 + 12y + 4y2)

Solving
135 = 9 + 12y + 4y2

Solving for variable 'y'.

Combine like terms: 135 + -9 = 126
126 + -12y + -4y2 = 9 + 12y + 4y2 + -9 + -12y + -4y2

Reorder the terms:
126 + -12y + -4y2 = 9 + -9 + 12y + -12y + 4y2 + -4y2

Combine like terms: 9 + -9 = 0
126 + -12y + -4y2 = 0 + 12y + -12y + 4y2 + -4y2
126 + -12y + -4y2 = 12y + -12y + 4y2 + -4y2

Combine like terms: 12y + -12y = 0
126 + -12y + -4y2 = 0 + 4y2 + -4y2
126 + -12y + -4y2 = 4y2 + -4y2

Combine like terms: 4y2 + -4y2 = 0
126 + -12y + -4y2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(63 + -6y + -2y2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(63 + -6y + -2y2)' equal to zero and attempt to solve:

Simplifying
63 + -6y + -2y2 = 0

Solving
63 + -6y + -2y2 = 0

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

Divide each side by '-2'.
-31.5 + 3y + y2 = 0

Move the constant term to the right:

Add '31.5' to each side of the equation.
-31.5 + 3y + 31.5 + y2 = 0 + 31.5

Reorder the terms:
-31.5 + 31.5 + 3y + y2 = 0 + 31.5

Combine like terms: -31.5 + 31.5 = 0.0
0.0 + 3y + y2 = 0 + 31.5
3y + y2 = 0 + 31.5

Combine like terms: 0 + 31.5 = 31.5
3y + y2 = 31.5

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 = 31.5 + 2.25

Reorder the terms:
2.25 + 3y + y2 = 31.5 + 2.25

Combine like terms: 31.5 + 2.25 = 33.75
2.25 + 3y + y2 = 33.75

Factor a perfect square on the left side:
(y + 1.5)(y + 1.5) = 33.75

Calculate the square root of the right side: 5.809475019

Break this problem into two subproblems by setting 
(y + 1.5) equal to 5.809475019 and -5.809475019.

Subproblem 1
y + 1.5 = 5.809475019

Simplifying
y + 1.5 = 5.809475019

Reorder the terms:
1.5 + y = 5.809475019

Solving
1.5 + y = 5.809475019

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 = 5.809475019 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + y = 5.809475019 + -1.5
y = 5.809475019 + -1.5

Combine like terms: 5.809475019 + -1.5 = 4.309475019
y = 4.309475019

Simplifying
y = 4.309475019

Subproblem 2
y + 1.5 = -5.809475019

Simplifying
y + 1.5 = -5.809475019

Reorder the terms:
1.5 + y = -5.809475019

Solving
1.5 + y = -5.809475019

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 = -5.809475019 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + y = -5.809475019 + -1.5
y = -5.809475019 + -1.5

Combine like terms: -5.809475019 + -1.5 = -7.309475019
y = -7.309475019

Simplifying
y = -7.309475019

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {4.309475019, -7.309475019}
Solution
y = {4.309475019, -7.309475019}