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Simplifying 9t3 + -27t2 + -2142t = 0 Reorder the terms: -2142t + -27t2 + 9t3 = 0 Solving -2142t + -27t2 + 9t3 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '9t'. 9t(-238 + -3t + t2) = 0 Factor a trinomial. 9t((-14 + -1t)(17 + -1t)) = 0 Ignore the factor 9.Subproblem 1
Set the factor 't' equal to zero and attempt to solve: Simplifying t = 0 Solving t = 0 Move all terms containing t to the left, all other terms to the right. Simplifying t = 0Subproblem 2
Set the factor '(-14 + -1t)' equal to zero and attempt to solve: Simplifying -14 + -1t = 0 Solving -14 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + -1t = 0 + 14 Combine like terms: -14 + 14 = 0 0 + -1t = 0 + 14 -1t = 0 + 14 Combine like terms: 0 + 14 = 14 -1t = 14 Divide each side by '-1'. t = -14 Simplifying t = -14Subproblem 3
Set the factor '(17 + -1t)' equal to zero and attempt to solve: Simplifying 17 + -1t = 0 Solving 17 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-17' to each side of the equation. 17 + -17 + -1t = 0 + -17 Combine like terms: 17 + -17 = 0 0 + -1t = 0 + -17 -1t = 0 + -17 Combine like terms: 0 + -17 = -17 -1t = -17 Divide each side by '-1'. t = 17 Simplifying t = 17Solution
t = {0, -14, 17}
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