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Simplifying 216 = -16t2 + -24t + 216 Reorder the terms: 216 = 216 + -24t + -16t2 Add '-216' to each side of the equation. 216 + -216 = 216 + -24t + -216 + -16t2 Combine like terms: 216 + -216 = 0 0 = 216 + -24t + -216 + -16t2 Reorder the terms: 0 = 216 + -216 + -24t + -16t2 Combine like terms: 216 + -216 = 0 0 = 0 + -24t + -16t2 0 = -24t + -16t2 Solving 0 = -24t + -16t2 Solving for variable 't'. Remove the zero: 24t + 16t2 = -24t + -16t2 + 24t + 16t2 Reorder the terms: 24t + 16t2 = -24t + 24t + -16t2 + 16t2 Combine like terms: -24t + 24t = 0 24t + 16t2 = 0 + -16t2 + 16t2 24t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 24t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '8t'. 8t(3 + 2t) = 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 '(3 + 2t)' equal to zero and attempt to solve: Simplifying 3 + 2t = 0 Solving 3 + 2t = 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 + 2t = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2t = 0 + -3 2t = 0 + -3 Combine like terms: 0 + -3 = -3 2t = -3 Divide each side by '2'. t = -1.5 Simplifying t = -1.5Solution
t = {0, -1.5}
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