8x^4y-16x^3y^2+24x^5=0

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Solution for 8x^4y-16x^3y^2+24x^5=0 equation: 


Simplifying
8x4y + -16x3y2 + 24x5 = 0

Reorder the terms:
-16x3y2 + 8x4y + 24x5 = 0

Solving
-16x3y2 + 8x4y + 24x5 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '8x3'.
8x3(-2y2 + xy + 3x2) = 0

Factor a trinomial.
8x3((-1y + -1x)(2y + -3x)) = 0

Ignore the factor 8.

Subproblem 1
Set the factor 'x3' equal to zero and attempt to solve:

Simplifying
x3 = 0

Solving
x3 = 0

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

Simplifying
x3 = 0

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 '(-1y + -1x)' equal to zero and attempt to solve:

Simplifying
-1y + -1x = 0

Reorder the terms:
-1x + -1y = 0

Solving
-1x + -1y = 0

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

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

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

Divide each side by '-1'.
x = -1y

Simplifying
x = -1y

Subproblem 3
Set the factor '(2y + -3x)' equal to zero and attempt to solve:

Simplifying
2y + -3x = 0

Reorder the terms:
-3x + 2y = 0

Solving
-3x + 2y = 0

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

Add '-2y' to each side of the equation.
-3x + 2y + -2y = 0 + -2y

Combine like terms: 2y + -2y = 0
-3x + 0 = 0 + -2y
-3x = 0 + -2y
Remove the zero:
-3x = -2y

Divide each side by '-3'.
x = 0.6666666667y

Simplifying
x = 0.6666666667y
Solution
x = {-1y, 0.6666666667y}

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