6y^3-10y^2+15y=0

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Solution for 6y^3-10y^2+15y=0 equation: 


Simplifying
6y3 + -10y2 + 15y = 0

Reorder the terms:
15y + -10y2 + 6y3 = 0

Solving
15y + -10y2 + 6y3 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), 'y'.
y(15 + -10y + 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 '(15 + -10y + 6y2)' equal to zero and attempt to solve:

Simplifying
15 + -10y + 6y2 = 0

Solving
15 + -10y + 6y2 = 0

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

Divide each side by '6'.
2.5 + -1.666666667y + y2 = 0

Move the constant term to the right:

Add '-2.5' to each side of the equation.
2.5 + -1.666666667y + -2.5 + y2 = 0 + -2.5

Reorder the terms:
2.5 + -2.5 + -1.666666667y + y2 = 0 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + -1.666666667y + y2 = 0 + -2.5
-1.666666667y + y2 = 0 + -2.5

Combine like terms: 0 + -2.5 = -2.5
-1.666666667y + y2 = -2.5

The y term is -1.666666667y.  Take half its coefficient (-0.8333333335).
Square it (0.6944444447) and add it to both sides.

Add '0.6944444447' to each side of the equation.
-1.666666667y + 0.6944444447 + y2 = -2.5 + 0.6944444447

Reorder the terms:
0.6944444447 + -1.666666667y + y2 = -2.5 + 0.6944444447

Combine like terms: -2.5 + 0.6944444447 = -1.8055555553
0.6944444447 + -1.666666667y + y2 = -1.8055555553

Factor a perfect square on the left side:
(y + -0.8333333335)(y + -0.8333333335) = -1.8055555553

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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