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Simplifying 6x3 + -168x2 + 162x = 0 Reorder the terms: 162x + -168x2 + 6x3 = 0 Solving 162x + -168x2 + 6x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '6x'. 6x(27 + -28x + x2) = 0 Factor a trinomial. 6x((1 + -1x)(27 + -1x)) = 0 Ignore the factor 6.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 '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Divide each side by '-1'. x = 1 Simplifying x = 1Subproblem 3
Set the factor '(27 + -1x)' equal to zero and attempt to solve: Simplifying 27 + -1x = 0 Solving 27 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-27' to each side of the equation. 27 + -27 + -1x = 0 + -27 Combine like terms: 27 + -27 = 0 0 + -1x = 0 + -27 -1x = 0 + -27 Combine like terms: 0 + -27 = -27 -1x = -27 Divide each side by '-1'. x = 27 Simplifying x = 27Solution
x = {0, 1, 27}
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