32x^5y^2-48x^4y^3-32x^3y^4=0

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Solution for 32x^5y^2-48x^4y^3-32x^3y^4=0 equation:


Simplifying
32x5y2 + -48x4y3 + -32x3y4 = 0

Reorder the terms:
-32x3y4 + -48x4y3 + 32x5y2 = 0

Solving
-32x3y4 + -48x4y3 + 32x5y2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '16x3y2'.
16x3y2(-2y2 + -3xy + 2x2) = 0

Factor a trinomial.
16x3y2((-1y + -2x)(2y + -1x)) = 0

Ignore the factor 16.

Subproblem 1

Set the factor 'x3y2' equal to zero and attempt to solve: Simplifying x3y2 = 0 Solving x3y2 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x3y2 = 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 + -2x)' equal to zero and attempt to solve: Simplifying -1y + -2x = 0 Reorder the terms: -2x + -1y = 0 Solving -2x + -1y = 0 Move all terms containing x to the left, all other terms to the right. Add 'y' to each side of the equation. -2x + -1y + y = 0 + y Combine like terms: -1y + y = 0 -2x + 0 = 0 + y -2x = 0 + y Remove the zero: -2x = y Divide each side by '-2'. x = -0.5y Simplifying x = -0.5y

Subproblem 3

Set the factor '(2y + -1x)' equal to zero and attempt to solve: Simplifying 2y + -1x = 0 Reorder the terms: -1x + 2y = 0 Solving -1x + 2y = 0 Move all terms containing x to the left, all other terms to the right. Add '-2y' to each side of the equation. -1x + 2y + -2y = 0 + -2y Combine like terms: 2y + -2y = 0 -1x + 0 = 0 + -2y -1x = 0 + -2y Remove the zero: -1x = -2y Divide each side by '-1'. x = 2y Simplifying x = 2y

Solution

x = {-0.5y, 2y}

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