y^3-5ay^2+6a^2y=0

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Solution for y^3-5ay^2+6a^2y=0 equation: 


Simplifying
y3 + -5ay2 + 6a2y = 0

Reorder the terms:
-5ay2 + 6a2y + y3 = 0

Solving
-5ay2 + 6a2y + y3 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), 'y'.
y(-5ay + 6a2 + y2) = 0

Factor a trinomial.
y((2a + -1y)(3a + -1y)) = 0


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

Simplifying
y = 0

Solving
y = 0

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

Add '-1y' to each side of the equation.
y + -1y = 0 + -1y
Remove the zero:
0 = -1y

Simplifying
0 = -1y

The solution to this equation could not be determined.

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

Subproblem 2
Set the factor '(2a + -1y)' equal to zero and attempt to solve:

Simplifying
2a + -1y = 0

Solving
2a + -1y = 0

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

Add 'y' to each side of the equation.
2a + -1y + y = 0 + y

Combine like terms: -1y + y = 0
2a + 0 = 0 + y
2a = 0 + y
Remove the zero:
2a = y

Divide each side by '2'.
a = 0.5y

Simplifying
a = 0.5y

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

Simplifying
3a + -1y = 0

Solving
3a + -1y = 0

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

Add 'y' to each side of the equation.
3a + -1y + y = 0 + y

Combine like terms: -1y + y = 0
3a + 0 = 0 + y
3a = 0 + y
Remove the zero:
3a = y

Divide each side by '3'.
a = 0.3333333333y

Simplifying
a = 0.3333333333y
Solution
a = {0.5y, 0.3333333333y}

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