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Simplifying 9(x2 + -3x) = 3x(x2 + -6x + 9) Reorder the terms: 9(-3x + x2) = 3x(x2 + -6x + 9) (-3x * 9 + x2 * 9) = 3x(x2 + -6x + 9) (-27x + 9x2) = 3x(x2 + -6x + 9) Reorder the terms: -27x + 9x2 = 3x(9 + -6x + x2) -27x + 9x2 = (9 * 3x + -6x * 3x + x2 * 3x) -27x + 9x2 = (27x + -18x2 + 3x3) Solving -27x + 9x2 = 27x + -18x2 + 3x3 Solving for variable 'x'. Reorder the terms: -27x + -27x + 9x2 + 18x2 + -3x3 = 27x + -18x2 + 3x3 + -27x + 18x2 + -3x3 Combine like terms: -27x + -27x = -54x -54x + 9x2 + 18x2 + -3x3 = 27x + -18x2 + 3x3 + -27x + 18x2 + -3x3 Combine like terms: 9x2 + 18x2 = 27x2 -54x + 27x2 + -3x3 = 27x + -18x2 + 3x3 + -27x + 18x2 + -3x3 Reorder the terms: -54x + 27x2 + -3x3 = 27x + -27x + -18x2 + 18x2 + 3x3 + -3x3 Combine like terms: 27x + -27x = 0 -54x + 27x2 + -3x3 = 0 + -18x2 + 18x2 + 3x3 + -3x3 -54x + 27x2 + -3x3 = -18x2 + 18x2 + 3x3 + -3x3 Combine like terms: -18x2 + 18x2 = 0 -54x + 27x2 + -3x3 = 0 + 3x3 + -3x3 -54x + 27x2 + -3x3 = 3x3 + -3x3 Combine like terms: 3x3 + -3x3 = 0 -54x + 27x2 + -3x3 = 0 Factor out the Greatest Common Factor (GCF), '3x'. 3x(-18 + 9x + -1x2) = 0 Factor a trinomial. 3x((-6 + x)(3 + -1x)) = 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 '(-6 + x)' equal to zero and attempt to solve: Simplifying -6 + x = 0 Solving -6 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = 0 + 6 Combine like terms: -6 + 6 = 0 0 + x = 0 + 6 x = 0 + 6 Combine like terms: 0 + 6 = 6 x = 6 Simplifying x = 6Subproblem 3
Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3Solution
x = {0, 6, 3}
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