6y(8y-4)=22

Solution for 6y(8y-4)=22 equation:

Simplifying
6y(8y + -4) = 22

Reorder the terms:
6y(-4 + 8y) = 22
(-4 * 6y + 8y * 6y) = 22
(-24y + 48y2) = 22

Solving
-24y + 48y2 = 22

Solving for variable 'y'.

Reorder the terms:
-22 + -24y + 48y2 = 22 + -22

Combine like terms: 22 + -22 = 0
-22 + -24y + 48y2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-11 + -12y + 24y2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-11 + -12y + 24y2)' equal to zero and attempt to solve:

Simplifying
-11 + -12y + 24y2 = 0

Solving
-11 + -12y + 24y2 = 0

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

Divide each side by '24'.
-0.4583333333 + -0.5y + y2 = 0

Move the constant term to the right:

Add '0.4583333333' to each side of the equation.
-0.4583333333 + -0.5y + 0.4583333333 + y2 = 0 + 0.4583333333

Reorder the terms:
-0.4583333333 + 0.4583333333 + -0.5y + y2 = 0 + 0.4583333333

Combine like terms: -0.4583333333 + 0.4583333333 = 0.0000000000
0.0000000000 + -0.5y + y2 = 0 + 0.4583333333
-0.5y + y2 = 0 + 0.4583333333

Combine like terms: 0 + 0.4583333333 = 0.4583333333
-0.5y + y2 = 0.4583333333

The y term is -0.5y.  Take half its coefficient (-0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
-0.5y + 0.0625 + y2 = 0.4583333333 + 0.0625

Reorder the terms:
0.0625 + -0.5y + y2 = 0.4583333333 + 0.0625

Combine like terms: 0.4583333333 + 0.0625 = 0.5208333333
0.0625 + -0.5y + y2 = 0.5208333333

Factor a perfect square on the left side:
(y + -0.25)(y + -0.25) = 0.5208333333

Calculate the square root of the right side: 0.721687836

Break this problem into two subproblems by setting 
(y + -0.25) equal to 0.721687836 and -0.721687836.

Subproblem 1
y + -0.25 = 0.721687836

Simplifying
y + -0.25 = 0.721687836

Reorder the terms:
-0.25 + y = 0.721687836

Solving
-0.25 + y = 0.721687836

Solving for variable 'y'.

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

Add '0.25' to each side of the equation.
-0.25 + 0.25 + y = 0.721687836 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + y = 0.721687836 + 0.25
y = 0.721687836 + 0.25

Combine like terms: 0.721687836 + 0.25 = 0.971687836
y = 0.971687836

Simplifying
y = 0.971687836

Subproblem 2
y + -0.25 = -0.721687836

Simplifying
y + -0.25 = -0.721687836

Reorder the terms:
-0.25 + y = -0.721687836

Solving
-0.25 + y = -0.721687836

Solving for variable 'y'.

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

Add '0.25' to each side of the equation.
-0.25 + 0.25 + y = -0.721687836 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + y = -0.721687836 + 0.25
y = -0.721687836 + 0.25

Combine like terms: -0.721687836 + 0.25 = -0.471687836
y = -0.471687836

Simplifying
y = -0.471687836

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {0.971687836, -0.471687836}
Solution
y = {0.971687836, -0.471687836}