12y*5(y-6)=4

Solution for 12y*5(y-6)=4 equation:

Simplifying
12y * 5(y + -6) = 4

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

Reorder the terms for easier multiplication:
12 * 5y(-6 + y) = 4

Multiply 12 * 5
60y(-6 + y) = 4
(-6 * 60y + y * 60y) = 4
(-360y + 60y2) = 4

Solving
-360y + 60y2 = 4

Solving for variable 'y'.

Reorder the terms:
-4 + -360y + 60y2 = 4 + -4

Combine like terms: 4 + -4 = 0
-4 + -360y + 60y2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-1 + -90y + 15y2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-1 + -90y + 15y2)' equal to zero and attempt to solve:

Simplifying
-1 + -90y + 15y2 = 0

Solving
-1 + -90y + 15y2 = 0

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

Divide each side by '15'.
-0.06666666667 + -6y + y2 = 0

Move the constant term to the right:

Add '0.06666666667' to each side of the equation.
-0.06666666667 + -6y + 0.06666666667 + y2 = 0 + 0.06666666667

Reorder the terms:
-0.06666666667 + 0.06666666667 + -6y + y2 = 0 + 0.06666666667

Combine like terms: -0.06666666667 + 0.06666666667 = 0.00000000000
0.00000000000 + -6y + y2 = 0 + 0.06666666667
-6y + y2 = 0 + 0.06666666667

Combine like terms: 0 + 0.06666666667 = 0.06666666667
-6y + y2 = 0.06666666667

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 = 0.06666666667 + 9

Reorder the terms:
9 + -6y + y2 = 0.06666666667 + 9

Combine like terms: 0.06666666667 + 9 = 9.06666666667
9 + -6y + y2 = 9.06666666667

Factor a perfect square on the left side:
(y + -3)(y + -3) = 9.06666666667

Calculate the square root of the right side: 3.011090611

Break this problem into two subproblems by setting 
(y + -3) equal to 3.011090611 and -3.011090611.

Subproblem 1
y + -3 = 3.011090611

Simplifying
y + -3 = 3.011090611

Reorder the terms:
-3 + y = 3.011090611

Solving
-3 + y = 3.011090611

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 = 3.011090611 + 3

Combine like terms: -3 + 3 = 0
0 + y = 3.011090611 + 3
y = 3.011090611 + 3

Combine like terms: 3.011090611 + 3 = 6.011090611
y = 6.011090611

Simplifying
y = 6.011090611

Subproblem 2
y + -3 = -3.011090611

Simplifying
y + -3 = -3.011090611

Reorder the terms:
-3 + y = -3.011090611

Solving
-3 + y = -3.011090611

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 = -3.011090611 + 3

Combine like terms: -3 + 3 = 0
0 + y = -3.011090611 + 3
y = -3.011090611 + 3

Combine like terms: -3.011090611 + 3 = -0.011090611
y = -0.011090611

Simplifying
y = -0.011090611

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {6.011090611, -0.011090611}
Solution
y = {6.011090611, -0.011090611}