6(y-3)2(y-3)-15=0

Solution for 6(y-3)2(y-3)-15=0 equation:

Simplifying
6(y + -3) * 2(y + -3) + -15 = 0

Reorder the terms:
6(-3 + y) * 2(y + -3) + -15 = 0

Reorder the terms:
6(-3 + y) * 2(-3 + y) + -15 = 0

Reorder the terms for easier multiplication:
6 * 2(-3 + y)(-3 + y) + -15 = 0

Multiply 6 * 2
12(-3 + y)(-3 + y) + -15 = 0

Multiply (-3 + y) * (-3 + y)
12(-3(-3 + y) + y(-3 + y)) + -15 = 0
12((-3 * -3 + y * -3) + y(-3 + y)) + -15 = 0
12((9 + -3y) + y(-3 + y)) + -15 = 0
12(9 + -3y + (-3 * y + y * y)) + -15 = 0
12(9 + -3y + (-3y + y2)) + -15 = 0

Combine like terms: -3y + -3y = -6y
12(9 + -6y + y2) + -15 = 0
(9 * 12 + -6y * 12 + y2 * 12) + -15 = 0
(108 + -72y + 12y2) + -15 = 0

Reorder the terms:
108 + -15 + -72y + 12y2 = 0

Combine like terms: 108 + -15 = 93
93 + -72y + 12y2 = 0

Solving
93 + -72y + 12y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '3'.
3(31 + -24y + 4y2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(31 + -24y + 4y2)' equal to zero and attempt to solve:

Simplifying
31 + -24y + 4y2 = 0

Solving
31 + -24y + 4y2 = 0

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

Divide each side by '4'.
7.75 + -6y + y2 = 0

Move the constant term to the right:

Add '-7.75' to each side of the equation.
7.75 + -6y + -7.75 + y2 = 0 + -7.75

Reorder the terms:
7.75 + -7.75 + -6y + y2 = 0 + -7.75

Combine like terms: 7.75 + -7.75 = 0.00
0.00 + -6y + y2 = 0 + -7.75
-6y + y2 = 0 + -7.75

Combine like terms: 0 + -7.75 = -7.75
-6y + y2 = -7.75

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 = -7.75 + 9

Reorder the terms:
9 + -6y + y2 = -7.75 + 9

Combine like terms: -7.75 + 9 = 1.25
9 + -6y + y2 = 1.25

Factor a perfect square on the left side:
(y + -3)(y + -3) = 1.25

Calculate the square root of the right side: 1.118033989

Break this problem into two subproblems by setting 
(y + -3) equal to 1.118033989 and -1.118033989.

Subproblem 1
y + -3 = 1.118033989

Simplifying
y + -3 = 1.118033989

Reorder the terms:
-3 + y = 1.118033989

Solving
-3 + y = 1.118033989

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 = 1.118033989 + 3

Combine like terms: -3 + 3 = 0
0 + y = 1.118033989 + 3
y = 1.118033989 + 3

Combine like terms: 1.118033989 + 3 = 4.118033989
y = 4.118033989

Simplifying
y = 4.118033989

Subproblem 2
y + -3 = -1.118033989

Simplifying
y + -3 = -1.118033989

Reorder the terms:
-3 + y = -1.118033989

Solving
-3 + y = -1.118033989

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 = -1.118033989 + 3

Combine like terms: -3 + 3 = 0
0 + y = -1.118033989 + 3
y = -1.118033989 + 3

Combine like terms: -1.118033989 + 3 = 1.881966011
y = 1.881966011

Simplifying
y = 1.881966011

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {4.118033989, 1.881966011}
Solution
y = {4.118033989, 1.881966011}