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Simplifying 8t3 + -24t2 + -2160t = 0 Reorder the terms: -2160t + -24t2 + 8t3 = 0 Solving -2160t + -24t2 + 8t3 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '8t'. 8t(-270 + -3t + t2) = 0 Factor a trinomial. 8t((-15 + -1t)(18 + -1t)) = 0 Ignore the factor 8.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 '(-15 + -1t)' equal to zero and attempt to solve: Simplifying -15 + -1t = 0 Solving -15 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + -1t = 0 + 15 Combine like terms: -15 + 15 = 0 0 + -1t = 0 + 15 -1t = 0 + 15 Combine like terms: 0 + 15 = 15 -1t = 15 Divide each side by '-1'. t = -15 Simplifying t = -15Subproblem 3
Set the factor '(18 + -1t)' equal to zero and attempt to solve: Simplifying 18 + -1t = 0 Solving 18 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-18' to each side of the equation. 18 + -18 + -1t = 0 + -18 Combine like terms: 18 + -18 = 0 0 + -1t = 0 + -18 -1t = 0 + -18 Combine like terms: 0 + -18 = -18 -1t = -18 Divide each side by '-1'. t = 18 Simplifying t = 18Solution
t = {0, -15, 18}
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