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Simplifying -16t2 + 24t + 864 = 432 Reorder the terms: 864 + 24t + -16t2 = 432 Solving 864 + 24t + -16t2 = 432 Solving for variable 't'. Reorder the terms: 864 + -432 + 24t + -16t2 = 432 + -432 Combine like terms: 864 + -432 = 432 432 + 24t + -16t2 = 432 + -432 Combine like terms: 432 + -432 = 0 432 + 24t + -16t2 = 0 Factor out the Greatest Common Factor (GCF), '8'. 8(54 + 3t + -2t2) = 0 Factor a trinomial. 8((6 + -1t)(9 + 2t)) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(6 + -1t)' equal to zero and attempt to solve: Simplifying 6 + -1t = 0 Solving 6 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1t = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1t = 0 + -6 -1t = 0 + -6 Combine like terms: 0 + -6 = -6 -1t = -6 Divide each side by '-1'. t = 6 Simplifying t = 6Subproblem 2
Set the factor '(9 + 2t)' equal to zero and attempt to solve: Simplifying 9 + 2t = 0 Solving 9 + 2t = 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 + 2t = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 2t = 0 + -9 2t = 0 + -9 Combine like terms: 0 + -9 = -9 2t = -9 Divide each side by '2'. t = -4.5 Simplifying t = -4.5Solution
t = {6, -4.5}
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