2x^3-2x^2y-12xy^2=0

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Solution for 2x^3-2x^2y-12xy^2=0 equation:


Simplifying
2x3 + -2x2y + -12xy2 = 0

Reorder the terms:
-12xy2 + -2x2y + 2x3 = 0

Solving
-12xy2 + -2x2y + 2x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x'.
2x(-6y2 + -1xy + x2) = 0

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

Ignore the factor 2.

Subproblem 1

Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0

Subproblem 2

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

Subproblem 3

Set the factor '(3y + -1x)' equal to zero and attempt to solve: Simplifying 3y + -1x = 0 Reorder the terms: -1x + 3y = 0 Solving -1x + 3y = 0 Move all terms containing x to the left, all other terms to the right. Add '-3y' to each side of the equation. -1x + 3y + -3y = 0 + -3y Combine like terms: 3y + -3y = 0 -1x + 0 = 0 + -3y -1x = 0 + -3y Remove the zero: -1x = -3y Divide each side by '-1'. x = 3y Simplifying x = 3y

Solution

x = {0, -2y, 3y}

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