Y^4-9Y^3+24Y^2=0

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Solution for Y^4-9Y^3+24Y^2=0 equation: 


Simplifying
Y4 + -9Y3 + 24Y2 = 0

Reorder the terms:
24Y2 + -9Y3 + Y4 = 0

Solving
24Y2 + -9Y3 + Y4 = 0

Solving for variable 'Y'.

Factor out the Greatest Common Factor (GCF), 'Y2'.
Y2(24 + -9Y + Y2) = 0


Subproblem 1
Set the factor 'Y2' equal to zero and attempt to solve:

Simplifying
Y2 = 0

Solving
Y2 = 0

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

Simplifying
Y2 = 0

Take the square root of each side:
Y = {0}

Subproblem 2
Set the factor '(24 + -9Y + Y2)' equal to zero and attempt to solve:

Simplifying
24 + -9Y + Y2 = 0

Solving
24 + -9Y + Y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-24' to each side of the equation.
24 + -9Y + -24 + Y2 = 0 + -24

Reorder the terms:
24 + -24 + -9Y + Y2 = 0 + -24

Combine like terms: 24 + -24 = 0
0 + -9Y + Y2 = 0 + -24
-9Y + Y2 = 0 + -24

Combine like terms: 0 + -24 = -24
-9Y + Y2 = -24

The Y term is -9Y.  Take half its coefficient (-4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
-9Y + 20.25 + Y2 = -24 + 20.25

Reorder the terms:
20.25 + -9Y + Y2 = -24 + 20.25

Combine like terms: -24 + 20.25 = -3.75
20.25 + -9Y + Y2 = -3.75

Factor a perfect square on the left side:
(Y + -4.5)(Y + -4.5) = -3.75

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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