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Simplifying 30x3 + 3x2y + -6xy2 = 0 Reorder the terms: -6xy2 + 3x2y + 30x3 = 0 Solving -6xy2 + 3x2y + 30x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3x'. 3x(-2y2 + xy + 10x2) = 0 Factor a trinomial. 3x((-1y + -2x)(2y + -5x)) = 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 = 0Subproblem 2
Set the factor '(-1y + -2x)' equal to zero and attempt to solve: Simplifying -1y + -2x = 0 Reorder the terms: -2x + -1y = 0 Solving -2x + -1y = 0 Move all terms containing x to the left, all other terms to the right. Add 'y' to each side of the equation. -2x + -1y + y = 0 + y Combine like terms: -1y + y = 0 -2x + 0 = 0 + y -2x = 0 + y Remove the zero: -2x = y Divide each side by '-2'. x = -0.5y Simplifying x = -0.5ySubproblem 3
Set the factor '(2y + -5x)' equal to zero and attempt to solve: Simplifying 2y + -5x = 0 Reorder the terms: -5x + 2y = 0 Solving -5x + 2y = 0 Move all terms containing x to the left, all other terms to the right. Add '-2y' to each side of the equation. -5x + 2y + -2y = 0 + -2y Combine like terms: 2y + -2y = 0 -5x + 0 = 0 + -2y -5x = 0 + -2y Remove the zero: -5x = -2y Divide each side by '-5'. x = 0.4y Simplifying x = 0.4ySolution
x = {0, -0.5y, 0.4y}
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