4y-28-2y-6y^2=6y^2

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Solution for 4y-28-2y-6y^2=6y^2 equation: 


Simplifying
4y + -28 + -2y + -6y2 = 6y2

Reorder the terms:
-28 + 4y + -2y + -6y2 = 6y2

Combine like terms: 4y + -2y = 2y
-28 + 2y + -6y2 = 6y2

Solving
-28 + 2y + -6y2 = 6y2

Solving for variable 'y'.

Combine like terms: -6y2 + -6y2 = -12y2
-28 + 2y + -12y2 = 6y2 + -6y2

Combine like terms: 6y2 + -6y2 = 0
-28 + 2y + -12y2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-14 + y + -6y2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-14 + y + -6y2)' equal to zero and attempt to solve:

Simplifying
-14 + y + -6y2 = 0

Solving
-14 + y + -6y2 = 0

Begin completing the square.  Divide all terms by
-6 the coefficient of the squared term: 

Divide each side by '-6'.
2.333333333 + -0.1666666667y + y2 = 0

Move the constant term to the right:

Add '-2.333333333' to each side of the equation.
2.333333333 + -0.1666666667y + -2.333333333 + y2 = 0 + -2.333333333

Reorder the terms:
2.333333333 + -2.333333333 + -0.1666666667y + y2 = 0 + -2.333333333

Combine like terms: 2.333333333 + -2.333333333 = 0.000000000
0.000000000 + -0.1666666667y + y2 = 0 + -2.333333333
-0.1666666667y + y2 = 0 + -2.333333333

Combine like terms: 0 + -2.333333333 = -2.333333333
-0.1666666667y + y2 = -2.333333333

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

Add '0.25' to each side of the equation.
-0.1666666667y + 0.25 + y2 = -2.333333333 + 0.25

Reorder the terms:
0.25 + -0.1666666667y + y2 = -2.333333333 + 0.25

Combine like terms: -2.333333333 + 0.25 = -2.083333333
0.25 + -0.1666666667y + y2 = -2.083333333

Factor a perfect square on the left side:
(y + 0.5)(y + 0.5) = -2.083333333

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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