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Simplifying 3xy2 + -27x3 = 0 Solving 3xy2 + -27x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3x'. 3x(y2 + -9x2) = 0 Factor a difference between two squares. 3x((y + 3x)(y + -3x)) = 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 '(y + 3x)' equal to zero and attempt to solve: Simplifying y + 3x = 0 Reorder the terms: 3x + y = 0 Solving 3x + y = 0 Move all terms containing x to the left, all other terms to the right. Add '-1y' to each side of the equation. 3x + y + -1y = 0 + -1y Combine like terms: y + -1y = 0 3x + 0 = 0 + -1y 3x = 0 + -1y Remove the zero: 3x = -1y Divide each side by '3'. x = -0.3333333333y Simplifying x = -0.3333333333ySubproblem 3
Set the factor '(y + -3x)' equal to zero and attempt to solve: Simplifying y + -3x = 0 Reorder the terms: -3x + y = 0 Solving -3x + y = 0 Move all terms containing x to the left, all other terms to the right. Add '-1y' to each side of the equation. -3x + y + -1y = 0 + -1y Combine like terms: y + -1y = 0 -3x + 0 = 0 + -1y -3x = 0 + -1y Remove the zero: -3x = -1y Divide each side by '-3'. x = 0.3333333333y Simplifying x = 0.3333333333ySolution
x = {0, -0.3333333333y, 0.3333333333y}
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