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Simplifying 216 = 96t + -8t2 Solving 216 = 96t + -8t2 Solving for variable 't'. Reorder the terms: 216 + -96t + 8t2 = 96t + -96t + -8t2 + 8t2 Combine like terms: 96t + -96t = 0 216 + -96t + 8t2 = 0 + -8t2 + 8t2 216 + -96t + 8t2 = -8t2 + 8t2 Combine like terms: -8t2 + 8t2 = 0 216 + -96t + 8t2 = 0 Factor out the Greatest Common Factor (GCF), '8'. 8(27 + -12t + t2) = 0 Factor a trinomial. 8((3 + -1t)(9 + -1t)) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(3 + -1t)' equal to zero and attempt to solve: Simplifying 3 + -1t = 0 Solving 3 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1t = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1t = 0 + -3 -1t = 0 + -3 Combine like terms: 0 + -3 = -3 -1t = -3 Divide each side by '-1'. t = 3 Simplifying t = 3Subproblem 2
Set the factor '(9 + -1t)' equal to zero and attempt to solve: Simplifying 9 + -1t = 0 Solving 9 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -1t = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1t = 0 + -9 -1t = 0 + -9 Combine like terms: 0 + -9 = -9 -1t = -9 Divide each side by '-1'. t = 9 Simplifying t = 9Solution
t = {3, 9}
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