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Simplifying 12xy2 + -36x2y + 27x3 = 0 Solving 12xy2 + -36x2y + 27x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3x'. 3x(4y2 + -12xy + 9x2) = 0 Factor a trinomial. 3x((2y + -3x)(2y + -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 '(2y + -3x)' equal to zero and attempt to solve: Simplifying 2y + -3x = 0 Reorder the terms: -3x + 2y = 0 Solving -3x + 2y = 0 Move all terms containing x to the left, all other terms to the right. Add '-2y' to each side of the equation. -3x + 2y + -2y = 0 + -2y Combine like terms: 2y + -2y = 0 -3x + 0 = 0 + -2y -3x = 0 + -2y Remove the zero: -3x = -2y Divide each side by '-3'. x = 0.6666666667y Simplifying x = 0.6666666667ySubproblem 3
Set the factor '(2y + -3x)' equal to zero and attempt to solve: Simplifying 2y + -3x = 0 Reorder the terms: -3x + 2y = 0 Solving -3x + 2y = 0 Move all terms containing x to the left, all other terms to the right. Add '-2y' to each side of the equation. -3x + 2y + -2y = 0 + -2y Combine like terms: 2y + -2y = 0 -3x + 0 = 0 + -2y -3x = 0 + -2y Remove the zero: -3x = -2y Divide each side by '-3'. x = 0.6666666667y Simplifying x = 0.6666666667ySolution
x = {0, 0.6666666667y, 0.6666666667y}
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