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Simplifying 0 = 6s3 + -21s2 + 9s Reorder the terms: 0 = 9s + -21s2 + 6s3 Solving 0 = 9s + -21s2 + 6s3 Solving for variable 's'. Remove the zero: -9s + 21s2 + -6s3 = 9s + -21s2 + 6s3 + -9s + 21s2 + -6s3 Reorder the terms: -9s + 21s2 + -6s3 = 9s + -9s + -21s2 + 21s2 + 6s3 + -6s3 Combine like terms: 9s + -9s = 0 -9s + 21s2 + -6s3 = 0 + -21s2 + 21s2 + 6s3 + -6s3 -9s + 21s2 + -6s3 = -21s2 + 21s2 + 6s3 + -6s3 Combine like terms: -21s2 + 21s2 = 0 -9s + 21s2 + -6s3 = 0 + 6s3 + -6s3 -9s + 21s2 + -6s3 = 6s3 + -6s3 Combine like terms: 6s3 + -6s3 = 0 -9s + 21s2 + -6s3 = 0 Factor out the Greatest Common Factor (GCF), '3s'. 3s(-3 + 7s + -2s2) = 0 Factor a trinomial. 3s((-3 + s)(1 + -2s)) = 0 Ignore the factor 3.Subproblem 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 '(-3 + s)' equal to zero and attempt to solve: Simplifying -3 + s = 0 Solving -3 + s = 0 Move all terms containing s to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + s = 0 + 3 Combine like terms: -3 + 3 = 0 0 + s = 0 + 3 s = 0 + 3 Combine like terms: 0 + 3 = 3 s = 3 Simplifying s = 3Subproblem 3
Set the factor '(1 + -2s)' equal to zero and attempt to solve: Simplifying 1 + -2s = 0 Solving 1 + -2s = 0 Move all terms containing s to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -2s = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2s = 0 + -1 -2s = 0 + -1 Combine like terms: 0 + -1 = -1 -2s = -1 Divide each side by '-2'. s = 0.5 Simplifying s = 0.5Solution
s = {0, 3, 0.5}
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