6y^2-20y+32=0

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Solution for 6y^2-20y+32=0 equation: 


Simplifying
6y2 + -20y + 32 = 0

Reorder the terms:
32 + -20y + 6y2 = 0

Solving
32 + -20y + 6y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '2'.
2(16 + -10y + 3y2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(16 + -10y + 3y2)' equal to zero and attempt to solve:

Simplifying
16 + -10y + 3y2 = 0

Solving
16 + -10y + 3y2 = 0

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

Divide each side by '3'.
5.333333333 + -3.333333333y + y2 = 0

Move the constant term to the right:

Add '-5.333333333' to each side of the equation.
5.333333333 + -3.333333333y + -5.333333333 + y2 = 0 + -5.333333333

Reorder the terms:
5.333333333 + -5.333333333 + -3.333333333y + y2 = 0 + -5.333333333

Combine like terms: 5.333333333 + -5.333333333 = 0.000000000
0.000000000 + -3.333333333y + y2 = 0 + -5.333333333
-3.333333333y + y2 = 0 + -5.333333333

Combine like terms: 0 + -5.333333333 = -5.333333333
-3.333333333y + y2 = -5.333333333

The y term is -3.333333333y.  Take half its coefficient (-1.666666667).
Square it (2.777777779) and add it to both sides.

Add '2.777777779' to each side of the equation.
-3.333333333y + 2.777777779 + y2 = -5.333333333 + 2.777777779

Reorder the terms:
2.777777779 + -3.333333333y + y2 = -5.333333333 + 2.777777779

Combine like terms: -5.333333333 + 2.777777779 = -2.555555554
2.777777779 + -3.333333333y + y2 = -2.555555554

Factor a perfect square on the left side:
(y + -1.666666667)(y + -1.666666667) = -2.555555554

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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