3(576y-1)(4y)=6912

Solution for 3(576y-1)(4y)=6912 equation:

Simplifying
3(576y + -1)(4y) = 6912

Reorder the terms:
3(-1 + 576y)(4y) = 6912

Remove parenthesis around (4y)
3(-1 + 576y) * 4y = 6912

Reorder the terms for easier multiplication:
3 * 4y(-1 + 576y) = 6912

Multiply 3 * 4
12y(-1 + 576y) = 6912
(-1 * 12y + 576y * 12y) = 6912
(-12y + 6912y2) = 6912

Solving
-12y + 6912y2 = 6912

Solving for variable 'y'.

Reorder the terms:
-6912 + -12y + 6912y2 = 6912 + -6912

Combine like terms: 6912 + -6912 = 0
-6912 + -12y + 6912y2 = 0

Factor out the Greatest Common Factor (GCF), '12'.
12(-576 + -1y + 576y2) = 0

Ignore the factor 12.
Subproblem 1
Set the factor '(-576 + -1y + 576y2)' equal to zero and attempt to solve:

Simplifying
-576 + -1y + 576y2 = 0

Solving
-576 + -1y + 576y2 = 0

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

Divide each side by '576'.
-1 + -0.001736111111y + y2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -0.001736111111y + 1 + y2 = 0 + 1

Reorder the terms:
-1 + 1 + -0.001736111111y + y2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -0.001736111111y + y2 = 0 + 1
-0.001736111111y + y2 = 0 + 1

Combine like terms: 0 + 1 = 1
-0.001736111111y + y2 = 1

The y term is -0.001736111111y.  Take half its coefficient (-0.0008680555555).
Square it (0.0000007535204474) and add it to both sides.

Add '0.0000007535204474' to each side of the equation.
-0.001736111111y + 0.0000007535204474 + y2 = 1 + 0.0000007535204474

Reorder the terms:
0.0000007535204474 + -0.001736111111y + y2 = 1 + 0.0000007535204474

Combine like terms: 1 + 0.0000007535204474 = 1.0000007535204474
0.0000007535204474 + -0.001736111111y + y2 = 1.0000007535204474

Factor a perfect square on the left side:
(y + -0.0008680555555)(y + -0.0008680555555) = 1.0000007535204474

Calculate the square root of the right side: 1.000000377

Break this problem into two subproblems by setting 
(y + -0.0008680555555) equal to 1.000000377 and -1.000000377.

Subproblem 1
y + -0.0008680555555 = 1.000000377

Simplifying
y + -0.0008680555555 = 1.000000377

Reorder the terms:
-0.0008680555555 + y = 1.000000377

Solving
-0.0008680555555 + y = 1.000000377

Solving for variable 'y'.

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

Add '0.0008680555555' to each side of the equation.
-0.0008680555555 + 0.0008680555555 + y = 1.000000377 + 0.0008680555555

Combine like terms: -0.0008680555555 + 0.0008680555555 = 0.0000000000000
0.0000000000000 + y = 1.000000377 + 0.0008680555555
y = 1.000000377 + 0.0008680555555

Combine like terms: 1.000000377 + 0.0008680555555 = 1.0008684325555
y = 1.0008684325555

Simplifying
y = 1.0008684325555

Subproblem 2
y + -0.0008680555555 = -1.000000377

Simplifying
y + -0.0008680555555 = -1.000000377

Reorder the terms:
-0.0008680555555 + y = -1.000000377

Solving
-0.0008680555555 + y = -1.000000377

Solving for variable 'y'.

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

Add '0.0008680555555' to each side of the equation.
-0.0008680555555 + 0.0008680555555 + y = -1.000000377 + 0.0008680555555

Combine like terms: -0.0008680555555 + 0.0008680555555 = 0.0000000000000
0.0000000000000 + y = -1.000000377 + 0.0008680555555
y = -1.000000377 + 0.0008680555555

Combine like terms: -1.000000377 + 0.0008680555555 = -0.9991323214445
y = -0.9991323214445

Simplifying
y = -0.9991323214445

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {1.0008684325555, -0.9991323214445}
Solution
y = {1.0008684325555, -0.9991323214445}