100(x^4)y-108(x^2)(y^3)-30(x^3)(y^2)=0

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Solution for 100(x^4)y-108(x^2)(y^3)-30(x^3)(y^2)=0 equation:


Simplifying
100(x4) * y + -108(x2)(y3) + -30(x3)(y2) = 0

Multiply x4 * y
100x4y + -108(x2)(y3) + -30(x3)(y2) = 0

Multiply x2 * y3
100x4y + -108x2y3 + -30(x3)(y2) = 0

Multiply x3 * y2
100x4y + -108x2y3 + -30x3y2 = 0

Reorder the terms:
-108x2y3 + -30x3y2 + 100x4y = 0

Solving
-108x2y3 + -30x3y2 + 100x4y = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x2y'.
2x2y(-54y2 + -15xy + 50x2) = 0

Factor a trinomial.
2x2y((-9y + -10x)(6y + -5x)) = 0

Ignore the factor 2.

Subproblem 1

Set the factor 'x2y' equal to zero and attempt to solve: Simplifying x2y = 0 Solving x2y = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x2y = 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 '(-9y + -10x)' equal to zero and attempt to solve: Simplifying -9y + -10x = 0 Reorder the terms: -10x + -9y = 0 Solving -10x + -9y = 0 Move all terms containing x to the left, all other terms to the right. Add '9y' to each side of the equation. -10x + -9y + 9y = 0 + 9y Combine like terms: -9y + 9y = 0 -10x + 0 = 0 + 9y -10x = 0 + 9y Remove the zero: -10x = 9y Divide each side by '-10'. x = -0.9y Simplifying x = -0.9y

Subproblem 3

Set the factor '(6y + -5x)' equal to zero and attempt to solve: Simplifying 6y + -5x = 0 Reorder the terms: -5x + 6y = 0 Solving -5x + 6y = 0 Move all terms containing x to the left, all other terms to the right. Add '-6y' to each side of the equation. -5x + 6y + -6y = 0 + -6y Combine like terms: 6y + -6y = 0 -5x + 0 = 0 + -6y -5x = 0 + -6y Remove the zero: -5x = -6y Divide each side by '-5'. x = 1.2y Simplifying x = 1.2y

Solution

x = {-0.9y, 1.2y}

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