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Simplifying 3x^{9}+ 6x^{8}+ -9x^{7}+ 6x^{6}= 0 Reorder the terms: 6x^{6}+ -9x^{7}+ 6x^{8}+ 3x^{9}= 0 Solving 6x^{6}+ -9x^{7}+ 6x^{8}+ 3x^{9}= 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3x^{6}'. 3x^{6}(2 + -3x + 2x^{2}+ x^{3}) = 0 Ignore the factor 3.## Subproblem 1

Set the factor 'x^{6}' equal to zero and attempt to solve: Simplifying x^{6}= 0 Solving x^{6}= 0 Move all terms containing x to the left, all other terms to the right. Simplifying x^{6}= 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 '(2 + -3x + 2x^{2}+ x^{3})' equal to zero and attempt to solve: Simplifying 2 + -3x + 2x^{2}+ x^{3}= 0 Solving 2 + -3x + 2x^{2}+ x^{3}= 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.

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