35x^3+120x^2y+45y^2x=0

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Solution for 35x^3+120x^2y+45y^2x=0 equation:


Simplifying
35x3 + 120x2y + 45y2x = 0

Reorder the terms:
45xy2 + 120x2y + 35x3 = 0

Solving
45xy2 + 120x2y + 35x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5x'.
5x(9y2 + 24xy + 7x2) = 0

Factor a trinomial.
5x((3y + x)(3y + 7x)) = 0

Ignore the factor 5.

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 '(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

Subproblem 3

Set the factor '(3y + 7x)' equal to zero and attempt to solve: Simplifying 3y + 7x = 0 Reorder the terms: 7x + 3y = 0 Solving 7x + 3y = 0 Move all terms containing x to the left, all other terms to the right. Add '-3y' to each side of the equation. 7x + 3y + -3y = 0 + -3y Combine like terms: 3y + -3y = 0 7x + 0 = 0 + -3y 7x = 0 + -3y Remove the zero: 7x = -3y Divide each side by '7'. x = -0.4285714286y Simplifying x = -0.4285714286y

Solution

x = {0, -3y, -0.4285714286y}

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