(2y-3)(2y-3)=63

Solution for (2y-3)(2y-3)=63 equation:

Simplifying
(2y + -3)(2y + -3) = 63

Reorder the terms:
(-3 + 2y)(2y + -3) = 63

Reorder the terms:
(-3 + 2y)(-3 + 2y) = 63

Multiply (-3 + 2y) * (-3 + 2y)
(-3(-3 + 2y) + 2y * (-3 + 2y)) = 63
((-3 * -3 + 2y * -3) + 2y * (-3 + 2y)) = 63
((9 + -6y) + 2y * (-3 + 2y)) = 63
(9 + -6y + (-3 * 2y + 2y * 2y)) = 63
(9 + -6y + (-6y + 4y2)) = 63

Combine like terms: -6y + -6y = -12y
(9 + -12y + 4y2) = 63

Solving
9 + -12y + 4y2 = 63

Solving for variable 'y'.

Reorder the terms:
9 + -63 + -12y + 4y2 = 63 + -63

Combine like terms: 9 + -63 = -54
-54 + -12y + 4y2 = 63 + -63

Combine like terms: 63 + -63 = 0
-54 + -12y + 4y2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-27 + -6y + 2y2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-27 + -6y + 2y2)' equal to zero and attempt to solve:

Simplifying
-27 + -6y + 2y2 = 0

Solving
-27 + -6y + 2y2 = 0

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

Divide each side by '2'.
-13.5 + -3y + y2 = 0

Move the constant term to the right:

Add '13.5' to each side of the equation.
-13.5 + -3y + 13.5 + y2 = 0 + 13.5

Reorder the terms:
-13.5 + 13.5 + -3y + y2 = 0 + 13.5

Combine like terms: -13.5 + 13.5 = 0.0
0.0 + -3y + y2 = 0 + 13.5
-3y + y2 = 0 + 13.5

Combine like terms: 0 + 13.5 = 13.5
-3y + y2 = 13.5

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 = 13.5 + 2.25

Reorder the terms:
2.25 + -3y + y2 = 13.5 + 2.25

Combine like terms: 13.5 + 2.25 = 15.75
2.25 + -3y + y2 = 15.75

Factor a perfect square on the left side:
(y + -1.5)(y + -1.5) = 15.75

Calculate the square root of the right side: 3.968626967

Break this problem into two subproblems by setting 
(y + -1.5) equal to 3.968626967 and -3.968626967.

Subproblem 1
y + -1.5 = 3.968626967

Simplifying
y + -1.5 = 3.968626967

Reorder the terms:
-1.5 + y = 3.968626967

Solving
-1.5 + y = 3.968626967

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 = 3.968626967 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + y = 3.968626967 + 1.5
y = 3.968626967 + 1.5

Combine like terms: 3.968626967 + 1.5 = 5.468626967
y = 5.468626967

Simplifying
y = 5.468626967

Subproblem 2
y + -1.5 = -3.968626967

Simplifying
y + -1.5 = -3.968626967

Reorder the terms:
-1.5 + y = -3.968626967

Solving
-1.5 + y = -3.968626967

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 = -3.968626967 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + y = -3.968626967 + 1.5
y = -3.968626967 + 1.5

Combine like terms: -3.968626967 + 1.5 = -2.468626967
y = -2.468626967

Simplifying
y = -2.468626967

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {5.468626967, -2.468626967}
Solution
y = {5.468626967, -2.468626967}