48y^2+104y=-660

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Solution for 48y^2+104y=-660 equation: 


Simplifying
48y2 + 104y = -660

Reorder the terms:
104y + 48y2 = -660

Solving
104y + 48y2 = -660

Solving for variable 'y'.

Reorder the terms:
660 + 104y + 48y2 = -660 + 660

Combine like terms: -660 + 660 = 0
660 + 104y + 48y2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(165 + 26y + 12y2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(165 + 26y + 12y2)' equal to zero and attempt to solve:

Simplifying
165 + 26y + 12y2 = 0

Solving
165 + 26y + 12y2 = 0

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

Divide each side by '12'.
13.75 + 2.166666667y + y2 = 0

Move the constant term to the right:

Add '-13.75' to each side of the equation.
13.75 + 2.166666667y + -13.75 + y2 = 0 + -13.75

Reorder the terms:
13.75 + -13.75 + 2.166666667y + y2 = 0 + -13.75

Combine like terms: 13.75 + -13.75 = 0.00
0.00 + 2.166666667y + y2 = 0 + -13.75
2.166666667y + y2 = 0 + -13.75

Combine like terms: 0 + -13.75 = -13.75
2.166666667y + y2 = -13.75

The y term is 2.166666667y.  Take half its coefficient (1.083333334).
Square it (1.173611113) and add it to both sides.

Add '1.173611113' to each side of the equation.
2.166666667y + 1.173611113 + y2 = -13.75 + 1.173611113

Reorder the terms:
1.173611113 + 2.166666667y + y2 = -13.75 + 1.173611113

Combine like terms: -13.75 + 1.173611113 = -12.576388887
1.173611113 + 2.166666667y + y2 = -12.576388887

Factor a perfect square on the left side:
(y + 1.083333334)(y + 1.083333334) = -12.576388887

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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