y^2-6+3y=4(y-5)(y-5)-12

Solution for y^2-6+3y=4(y-5)(y-5)-12 equation:

Simplifying
y2 + -6 + 3y = 4(y + -5)(y + -5) + -12

Reorder the terms:
-6 + 3y + y2 = 4(y + -5)(y + -5) + -12

Reorder the terms:
-6 + 3y + y2 = 4(-5 + y)(y + -5) + -12

Reorder the terms:
-6 + 3y + y2 = 4(-5 + y)(-5 + y) + -12

Multiply (-5 + y) * (-5 + y)
-6 + 3y + y2 = 4(-5(-5 + y) + y(-5 + y)) + -12
-6 + 3y + y2 = 4((-5 * -5 + y * -5) + y(-5 + y)) + -12
-6 + 3y + y2 = 4((25 + -5y) + y(-5 + y)) + -12
-6 + 3y + y2 = 4(25 + -5y + (-5 * y + y * y)) + -12
-6 + 3y + y2 = 4(25 + -5y + (-5y + y2)) + -12

Combine like terms: -5y + -5y = -10y
-6 + 3y + y2 = 4(25 + -10y + y2) + -12
-6 + 3y + y2 = (25 * 4 + -10y * 4 + y2 * 4) + -12
-6 + 3y + y2 = (100 + -40y + 4y2) + -12

Reorder the terms:
-6 + 3y + y2 = 100 + -12 + -40y + 4y2

Combine like terms: 100 + -12 = 88
-6 + 3y + y2 = 88 + -40y + 4y2

Solving
-6 + 3y + y2 = 88 + -40y + 4y2

Solving for variable 'y'.

Reorder the terms:
-6 + -88 + 3y + 40y + y2 + -4y2 = 88 + -40y + 4y2 + -88 + 40y + -4y2

Combine like terms: -6 + -88 = -94
-94 + 3y + 40y + y2 + -4y2 = 88 + -40y + 4y2 + -88 + 40y + -4y2

Combine like terms: 3y + 40y = 43y
-94 + 43y + y2 + -4y2 = 88 + -40y + 4y2 + -88 + 40y + -4y2

Combine like terms: y2 + -4y2 = -3y2
-94 + 43y + -3y2 = 88 + -40y + 4y2 + -88 + 40y + -4y2

Reorder the terms:
-94 + 43y + -3y2 = 88 + -88 + -40y + 40y + 4y2 + -4y2

Combine like terms: 88 + -88 = 0
-94 + 43y + -3y2 = 0 + -40y + 40y + 4y2 + -4y2
-94 + 43y + -3y2 = -40y + 40y + 4y2 + -4y2

Combine like terms: -40y + 40y = 0
-94 + 43y + -3y2 = 0 + 4y2 + -4y2
-94 + 43y + -3y2 = 4y2 + -4y2

Combine like terms: 4y2 + -4y2 = 0
-94 + 43y + -3y2 = 0

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

Divide each side by '-3'.
31.33333333 + -14.33333333y + y2 = 0

Move the constant term to the right:

Add '-31.33333333' to each side of the equation.
31.33333333 + -14.33333333y + -31.33333333 + y2 = 0 + -31.33333333

Reorder the terms:
31.33333333 + -31.33333333 + -14.33333333y + y2 = 0 + -31.33333333

Combine like terms: 31.33333333 + -31.33333333 = 0.00000000
0.00000000 + -14.33333333y + y2 = 0 + -31.33333333
-14.33333333y + y2 = 0 + -31.33333333

Combine like terms: 0 + -31.33333333 = -31.33333333
-14.33333333y + y2 = -31.33333333

The y term is -14.33333333y.  Take half its coefficient (-7.166666665).
Square it (51.36111109) and add it to both sides.

Add '51.36111109' to each side of the equation.
-14.33333333y + 51.36111109 + y2 = -31.33333333 + 51.36111109

Reorder the terms:
51.36111109 + -14.33333333y + y2 = -31.33333333 + 51.36111109

Combine like terms: -31.33333333 + 51.36111109 = 20.02777776
51.36111109 + -14.33333333y + y2 = 20.02777776

Factor a perfect square on the left side:
(y + -7.166666665)(y + -7.166666665) = 20.02777776

Calculate the square root of the right side: 4.475240525

Break this problem into two subproblems by setting 
(y + -7.166666665) equal to 4.475240525 and -4.475240525.

Subproblem 1
y + -7.166666665 = 4.475240525

Simplifying
y + -7.166666665 = 4.475240525

Reorder the terms:
-7.166666665 + y = 4.475240525

Solving
-7.166666665 + y = 4.475240525

Solving for variable 'y'.

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

Add '7.166666665' to each side of the equation.
-7.166666665 + 7.166666665 + y = 4.475240525 + 7.166666665

Combine like terms: -7.166666665 + 7.166666665 = 0.000000000
0.000000000 + y = 4.475240525 + 7.166666665
y = 4.475240525 + 7.166666665

Combine like terms: 4.475240525 + 7.166666665 = 11.64190719
y = 11.64190719

Simplifying
y = 11.64190719

Subproblem 2
y + -7.166666665 = -4.475240525

Simplifying
y + -7.166666665 = -4.475240525

Reorder the terms:
-7.166666665 + y = -4.475240525

Solving
-7.166666665 + y = -4.475240525

Solving for variable 'y'.

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

Add '7.166666665' to each side of the equation.
-7.166666665 + 7.166666665 + y = -4.475240525 + 7.166666665

Combine like terms: -7.166666665 + 7.166666665 = 0.000000000
0.000000000 + y = -4.475240525 + 7.166666665
y = -4.475240525 + 7.166666665

Combine like terms: -4.475240525 + 7.166666665 = 2.69142614
y = 2.69142614

Simplifying
y = 2.69142614

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {11.64190719, 2.69142614}