-6y^2-56y+48=0

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Solution for -6y^2-56y+48=0 equation: 


Simplifying
-6y2 + -56y + 48 = 0

Reorder the terms:
48 + -56y + -6y2 = 0

Solving
48 + -56y + -6y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '2'.
2(24 + -28y + -3y2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(24 + -28y + -3y2)' equal to zero and attempt to solve:

Simplifying
24 + -28y + -3y2 = 0

Solving
24 + -28y + -3y2 = 0

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

Divide each side by '-3'.
-8 + 9.333333333y + y2 = 0

Move the constant term to the right:

Add '8' to each side of the equation.
-8 + 9.333333333y + 8 + y2 = 0 + 8

Reorder the terms:
-8 + 8 + 9.333333333y + y2 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + 9.333333333y + y2 = 0 + 8
9.333333333y + y2 = 0 + 8

Combine like terms: 0 + 8 = 8
9.333333333y + y2 = 8

The y term is 9.333333333y.  Take half its coefficient (4.666666667).
Square it (21.77777778) and add it to both sides.

Add '21.77777778' to each side of the equation.
9.333333333y + 21.77777778 + y2 = 8 + 21.77777778

Reorder the terms:
21.77777778 + 9.333333333y + y2 = 8 + 21.77777778

Combine like terms: 8 + 21.77777778 = 29.77777778
21.77777778 + 9.333333333y + y2 = 29.77777778

Factor a perfect square on the left side:
(y + 4.666666667)(y + 4.666666667) = 29.77777778

Calculate the square root of the right side: 5.456901848

Break this problem into two subproblems by setting 
(y + 4.666666667) equal to 5.456901848 and -5.456901848.


Subproblem 1
y + 4.666666667 = 5.456901848

Simplifying
y + 4.666666667 = 5.456901848

Reorder the terms:
4.666666667 + y = 5.456901848

Solving
4.666666667 + y = 5.456901848

Solving for variable 'y'.

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

Add '-4.666666667' to each side of the equation.
4.666666667 + -4.666666667 + y = 5.456901848 + -4.666666667

Combine like terms: 4.666666667 + -4.666666667 = 0.000000000
0.000000000 + y = 5.456901848 + -4.666666667
y = 5.456901848 + -4.666666667

Combine like terms: 5.456901848 + -4.666666667 = 0.790235181
y = 0.790235181

Simplifying
y = 0.790235181


Subproblem 2
y + 4.666666667 = -5.456901848

Simplifying
y + 4.666666667 = -5.456901848

Reorder the terms:
4.666666667 + y = -5.456901848

Solving
4.666666667 + y = -5.456901848

Solving for variable 'y'.

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

Add '-4.666666667' to each side of the equation.
4.666666667 + -4.666666667 + y = -5.456901848 + -4.666666667

Combine like terms: 4.666666667 + -4.666666667 = 0.000000000
0.000000000 + y = -5.456901848 + -4.666666667
y = -5.456901848 + -4.666666667

Combine like terms: -5.456901848 + -4.666666667 = -10.123568515
y = -10.123568515

Simplifying
y = -10.123568515


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {0.790235181, -10.123568515}
Solution
y = {0.790235181, -10.123568515}

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