x^3y-3x^2y^2-40xy^3=0

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Solution for x^3y-3x^2y^2-40xy^3=0 equation:


Simplifying
x3y + -3x2y2 + -40xy3 = 0

Reorder the terms:
-40xy3 + -3x2y2 + x3y = 0

Solving
-40xy3 + -3x2y2 + x3y = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'xy'.
xy(-40y2 + -3xy + x2) = 0

Factor a trinomial.
xy((-5y + -1x)(8y + -1x)) = 0

Subproblem 1

Set the factor 'xy' equal to zero and attempt to solve: Simplifying xy = 0 Solving xy = 0 Move all terms containing x to the left, all other terms to the right. Simplifying xy = 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 + -1x)' equal to zero and attempt to solve: Simplifying -5y + -1x = 0 Reorder the terms: -1x + -5y = 0 Solving -1x + -5y = 0 Move all terms containing x to the left, all other terms to the right. Add '5y' to each side of the equation. -1x + -5y + 5y = 0 + 5y Combine like terms: -5y + 5y = 0 -1x + 0 = 0 + 5y -1x = 0 + 5y Remove the zero: -1x = 5y Divide each side by '-1'. x = -5y Simplifying x = -5y

Subproblem 3

Set the factor '(8y + -1x)' equal to zero and attempt to solve: Simplifying 8y + -1x = 0 Reorder the terms: -1x + 8y = 0 Solving -1x + 8y = 0 Move all terms containing x to the left, all other terms to the right. Add '-8y' to each side of the equation. -1x + 8y + -8y = 0 + -8y Combine like terms: 8y + -8y = 0 -1x + 0 = 0 + -8y -1x = 0 + -8y Remove the zero: -1x = -8y Divide each side by '-1'. x = 8y Simplifying x = 8y

Solution

x = {-5y, 8y}

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