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Simplifying (s + -6)(s + -6)(s + -6) = 27(s + -8) Reorder the terms: (-6 + s)(s + -6)(s + -6) = 27(s + -8) Reorder the terms: (-6 + s)(-6 + s)(s + -6) = 27(s + -8) Reorder the terms: (-6 + s)(-6 + s)(-6 + s) = 27(s + -8) Multiply (-6 + s) * (-6 + s) (-6(-6 + s) + s(-6 + s))(-6 + s) = 27(s + -8) ((-6 * -6 + s * -6) + s(-6 + s))(-6 + s) = 27(s + -8) ((36 + -6s) + s(-6 + s))(-6 + s) = 27(s + -8) (36 + -6s + (-6 * s + s * s))(-6 + s) = 27(s + -8) (36 + -6s + (-6s + s2))(-6 + s) = 27(s + -8) Combine like terms: -6s + -6s = -12s (36 + -12s + s2)(-6 + s) = 27(s + -8) Multiply (36 + -12s + s2) * (-6 + s) (36(-6 + s) + -12s * (-6 + s) + s2(-6 + s)) = 27(s + -8) ((-6 * 36 + s * 36) + -12s * (-6 + s) + s2(-6 + s)) = 27(s + -8) ((-216 + 36s) + -12s * (-6 + s) + s2(-6 + s)) = 27(s + -8) (-216 + 36s + (-6 * -12s + s * -12s) + s2(-6 + s)) = 27(s + -8) (-216 + 36s + (72s + -12s2) + s2(-6 + s)) = 27(s + -8) (-216 + 36s + 72s + -12s2 + (-6 * s2 + s * s2)) = 27(s + -8) (-216 + 36s + 72s + -12s2 + (-6s2 + s3)) = 27(s + -8) Combine like terms: 36s + 72s = 108s (-216 + 108s + -12s2 + -6s2 + s3) = 27(s + -8) Combine like terms: -12s2 + -6s2 = -18s2 (-216 + 108s + -18s2 + s3) = 27(s + -8) Reorder the terms: -216 + 108s + -18s2 + s3 = 27(-8 + s) -216 + 108s + -18s2 + s3 = (-8 * 27 + s * 27) -216 + 108s + -18s2 + s3 = (-216 + 27s) Add '216' to each side of the equation. -216 + 108s + -18s2 + 216 + s3 = -216 + 216 + 27s Reorder the terms: -216 + 216 + 108s + -18s2 + s3 = -216 + 216 + 27s Combine like terms: -216 + 216 = 0 0 + 108s + -18s2 + s3 = -216 + 216 + 27s 108s + -18s2 + s3 = -216 + 216 + 27s Combine like terms: -216 + 216 = 0 108s + -18s2 + s3 = 0 + 27s 108s + -18s2 + s3 = 27s Solving 108s + -18s2 + s3 = 27s Solving for variable 's'. Reorder the terms: 108s + -27s + -18s2 + s3 = 27s + -27s Combine like terms: 108s + -27s = 81s 81s + -18s2 + s3 = 27s + -27s Combine like terms: 27s + -27s = 0 81s + -18s2 + s3 = 0 Factor out the Greatest Common Factor (GCF), 's'. s(81 + -18s + s2) = 0 Factor a trinomial. s((9 + -1s)(9 + -1s)) = 0Subproblem 1
Set the factor 's' equal to zero and attempt to solve: Simplifying s = 0 Solving s = 0 Move all terms containing s to the left, all other terms to the right. Simplifying s = 0Subproblem 2
Set the factor '(9 + -1s)' equal to zero and attempt to solve: Simplifying 9 + -1s = 0 Solving 9 + -1s = 0 Move all terms containing s to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -1s = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1s = 0 + -9 -1s = 0 + -9 Combine like terms: 0 + -9 = -9 -1s = -9 Divide each side by '-1'. s = 9 Simplifying s = 9Subproblem 3
Set the factor '(9 + -1s)' equal to zero and attempt to solve: Simplifying 9 + -1s = 0 Solving 9 + -1s = 0 Move all terms containing s to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -1s = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1s = 0 + -9 -1s = 0 + -9 Combine like terms: 0 + -9 = -9 -1s = -9 Divide each side by '-1'. s = 9 Simplifying s = 9Solution
s = {0, 9, 9}
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