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Simplifying 12s3 + 14s2 + 8s = 4s Reorder the terms: 8s + 14s2 + 12s3 = 4s Solving 8s + 14s2 + 12s3 = 4s Solving for variable 's'. Reorder the terms: 8s + -4s + 14s2 + 12s3 = 4s + -4s Combine like terms: 8s + -4s = 4s 4s + 14s2 + 12s3 = 4s + -4s Combine like terms: 4s + -4s = 0 4s + 14s2 + 12s3 = 0 Factor out the Greatest Common Factor (GCF), '2s'. 2s(2 + 7s + 6s2) = 0 Factor a trinomial. 2s((2 + 3s)(1 + 2s)) = 0 Ignore the factor 2.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 '(2 + 3s)' equal to zero and attempt to solve: Simplifying 2 + 3s = 0 Solving 2 + 3s = 0 Move all terms containing s to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + 3s = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 3s = 0 + -2 3s = 0 + -2 Combine like terms: 0 + -2 = -2 3s = -2 Divide each side by '3'. s = -0.6666666667 Simplifying s = -0.6666666667Subproblem 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, -0.6666666667, -0.5}
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