18x^4y+24x^3y^2-10x^2y^3=0

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Solution for 18x^4y+24x^3y^2-10x^2y^3=0 equation: 


Simplifying
18x4y + 24x3y2 + -10x2y3 = 0

Reorder the terms:
-10x2y3 + 24x3y2 + 18x4y = 0

Solving
-10x2y3 + 24x3y2 + 18x4y = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x2y'.
2x2y(-5y2 + 12xy + 9x2) = 0

Factor a trinomial.
2x2y((-5y + -3x)(y + -3x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor 'x2y' equal to zero and attempt to solve:

Simplifying
x2y = 0

Solving
x2y = 0

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

Simplifying
x2y = 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 '(-5y + -3x)' equal to zero and attempt to solve:

Simplifying
-5y + -3x = 0

Reorder the terms:
-3x + -5y = 0

Solving
-3x + -5y = 0

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

Add '5y' to each side of the equation.
-3x + -5y + 5y = 0 + 5y

Combine like terms: -5y + 5y = 0
-3x + 0 = 0 + 5y
-3x = 0 + 5y
Remove the zero:
-3x = 5y

Divide each side by '-3'.
x = -1.666666667y

Simplifying
x = -1.666666667y

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

Simplifying
y + -3x = 0

Reorder the terms:
-3x + y = 0

Solving
-3x + y = 0

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

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

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

Divide each side by '-3'.
x = 0.3333333333y

Simplifying
x = 0.3333333333y
Solution
x = {-1.666666667y, 0.3333333333y}

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