-6y^3+13y^2-8y=0

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Solution for -6y^3+13y^2-8y=0 equation: 


Simplifying
-6y3 + 13y2 + -8y = 0

Reorder the terms:
-8y + 13y2 + -6y3 = 0

Solving
-8y + 13y2 + -6y3 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), 'y'.
y(-8 + 13y + -6y2) = 0


Subproblem 1
Set the factor 'y' equal to zero and attempt to solve:

Simplifying
y = 0

Solving
y = 0

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

Simplifying
y = 0

Subproblem 2
Set the factor '(-8 + 13y + -6y2)' equal to zero and attempt to solve:

Simplifying
-8 + 13y + -6y2 = 0

Solving
-8 + 13y + -6y2 = 0

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

Divide each side by '-6'.
1.333333333 + -2.166666667y + y2 = 0

Move the constant term to the right:

Add '-1.333333333' to each side of the equation.
1.333333333 + -2.166666667y + -1.333333333 + y2 = 0 + -1.333333333

Reorder the terms:
1.333333333 + -1.333333333 + -2.166666667y + y2 = 0 + -1.333333333

Combine like terms: 1.333333333 + -1.333333333 = 0.000000000
0.000000000 + -2.166666667y + y2 = 0 + -1.333333333
-2.166666667y + y2 = 0 + -1.333333333

Combine like terms: 0 + -1.333333333 = -1.333333333
-2.166666667y + y2 = -1.333333333

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 = -1.333333333 + 1.173611113

Reorder the terms:
1.173611113 + -2.166666667y + y2 = -1.333333333 + 1.173611113

Combine like terms: -1.333333333 + 1.173611113 = -0.15972222
1.173611113 + -2.166666667y + y2 = -0.15972222

Factor a perfect square on the left side:
(y + -1.083333334)(y + -1.083333334) = -0.15972222

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.
Solution
y = {0}

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