3x^3+33x^2y+54xy^2=0

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Solution for 3x^3+33x^2y+54xy^2=0 equation:


Simplifying
3x3 + 33x2y + 54xy2 = 0

Reorder the terms:
54xy2 + 33x2y + 3x3 = 0

Solving
54xy2 + 33x2y + 3x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3x'.
3x(18y2 + 11xy + x2) = 0

Factor a trinomial.
3x((9y + x)(2y + x)) = 0

Ignore the factor 3.

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 '(9y + x)' equal to zero and attempt to solve: Simplifying 9y + x = 0 Reorder the terms: x + 9y = 0 Solving x + 9y = 0 Move all terms containing x to the left, all other terms to the right. Add '-9y' to each side of the equation. x + 9y + -9y = 0 + -9y Combine like terms: 9y + -9y = 0 x + 0 = 0 + -9y x = 0 + -9y Remove the zero: x = -9y Simplifying x = -9y

Subproblem 3

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

Solution

x = {0, -9y, -2y}

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