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Simplifying (3x + 1) = 27x3 + -27x2 + 9x + 1 Reorder the terms: (1 + 3x) = 27x3 + -27x2 + 9x + 1 Remove parenthesis around (1 + 3x) 1 + 3x = 27x3 + -27x2 + 9x + 1 Reorder the terms: 1 + 3x = 1 + 9x + -27x2 + 27x3 Add '-1' to each side of the equation. 1 + -1 + 3x = 1 + 9x + -27x2 + -1 + 27x3 Combine like terms: 1 + -1 = 0 0 + 3x = 1 + 9x + -27x2 + -1 + 27x3 3x = 1 + 9x + -27x2 + -1 + 27x3 Reorder the terms: 3x = 1 + -1 + 9x + -27x2 + 27x3 Combine like terms: 1 + -1 = 0 3x = 0 + 9x + -27x2 + 27x3 3x = 9x + -27x2 + 27x3 Solving 3x = 9x + -27x2 + 27x3 Solving for variable 'x'. Combine like terms: 3x + -9x = -6x -6x + 27x2 + -27x3 = 9x + -27x2 + 27x3 + -9x + 27x2 + -27x3 Reorder the terms: -6x + 27x2 + -27x3 = 9x + -9x + -27x2 + 27x2 + 27x3 + -27x3 Combine like terms: 9x + -9x = 0 -6x + 27x2 + -27x3 = 0 + -27x2 + 27x2 + 27x3 + -27x3 -6x + 27x2 + -27x3 = -27x2 + 27x2 + 27x3 + -27x3 Combine like terms: -27x2 + 27x2 = 0 -6x + 27x2 + -27x3 = 0 + 27x3 + -27x3 -6x + 27x2 + -27x3 = 27x3 + -27x3 Combine like terms: 27x3 + -27x3 = 0 -6x + 27x2 + -27x3 = 0 Factor out the Greatest Common Factor (GCF), '3x'. 3x(-2 + 9x + -9x2) = 0 Factor a trinomial. 3x((-2 + 3x)(1 + -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 '(-2 + 3x)' equal to zero and attempt to solve: Simplifying -2 + 3x = 0 Solving -2 + 3x = 0 Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + 3x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 3x = 0 + 2 3x = 0 + 2 Combine like terms: 0 + 2 = 2 3x = 2 Divide each side by '3'. x = 0.6666666667 Simplifying x = 0.6666666667Subproblem 3
Set the factor '(1 + -3x)' equal to zero and attempt to solve: Simplifying 1 + -3x = 0 Solving 1 + -3x = 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 + -3x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -3x = 0 + -1 -3x = 0 + -1 Combine like terms: 0 + -1 = -1 -3x = -1 Divide each side by '-3'. x = 0.3333333333 Simplifying x = 0.3333333333Solution
x = {0, 0.6666666667, 0.3333333333}
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