2x^3+14x^2y+24xy^2=0

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Solution for 2x^3+14x^2y+24xy^2=0 equation:


Simplifying
2x3 + 14x2y + 24xy2 = 0

Reorder the terms:
24xy2 + 14x2y + 2x3 = 0

Solving
24xy2 + 14x2y + 2x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x'.
2x(12y2 + 7xy + x2) = 0

Factor a trinomial.
2x((4y + x)(3y + x)) = 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 '(4y + x)' equal to zero and attempt to solve: Simplifying 4y + x = 0 Reorder the terms: x + 4y = 0 Solving x + 4y = 0 Move all terms containing x to the left, all other terms to the right. Add '-4y' to each side of the equation. x + 4y + -4y = 0 + -4y Combine like terms: 4y + -4y = 0 x + 0 = 0 + -4y x = 0 + -4y Remove the zero: x = -4y Simplifying x = -4y

Subproblem 3

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

Solution

x = {0, -4y, -3y}

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