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Simplifying 18x3 + 33x2y + -6xy2 = 0 Reorder the terms: -6xy2 + 33x2y + 18x3 = 0 Solving -6xy2 + 33x2y + 18x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3x'. 3x(-2y2 + 11xy + 6x2) = 0 Factor a trinomial. 3x((-2y + -1x)(y + -6x)) = 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 '(-2y + -1x)' equal to zero and attempt to solve: Simplifying -2y + -1x = 0 Reorder the terms: -1x + -2y = 0 Solving -1x + -2y = 0 Move all terms containing x to the left, all other terms to the right. Add '2y' to each side of the equation. -1x + -2y + 2y = 0 + 2y Combine like terms: -2y + 2y = 0 -1x + 0 = 0 + 2y -1x = 0 + 2y Remove the zero: -1x = 2y Divide each side by '-1'. x = -2y Simplifying x = -2ySubproblem 3
Set the factor '(y + -6x)' equal to zero and attempt to solve: Simplifying y + -6x = 0 Reorder the terms: -6x + y = 0 Solving -6x + y = 0 Move all terms containing x to the left, all other terms to the right. Add '-1y' to each side of the equation. -6x + y + -1y = 0 + -1y Combine like terms: y + -1y = 0 -6x + 0 = 0 + -1y -6x = 0 + -1y Remove the zero: -6x = -1y Divide each side by '-6'. x = 0.1666666667y Simplifying x = 0.1666666667ySolution
x = {0, -2y, 0.1666666667y}
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