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Simplifying 9t = -16t2 + 60t Reorder the terms: 9t = 60t + -16t2 Solving 9t = 60t + -16t2 Solving for variable 't'. Combine like terms: 9t + -60t = -51t -51t + 16t2 = 60t + -16t2 + -60t + 16t2 Reorder the terms: -51t + 16t2 = 60t + -60t + -16t2 + 16t2 Combine like terms: 60t + -60t = 0 -51t + 16t2 = 0 + -16t2 + 16t2 -51t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -51t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), 't'. t(-51 + 16t) = 0Subproblem 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 '(-51 + 16t)' equal to zero and attempt to solve: Simplifying -51 + 16t = 0 Solving -51 + 16t = 0 Move all terms containing t to the left, all other terms to the right. Add '51' to each side of the equation. -51 + 51 + 16t = 0 + 51 Combine like terms: -51 + 51 = 0 0 + 16t = 0 + 51 16t = 0 + 51 Combine like terms: 0 + 51 = 51 16t = 51 Divide each side by '16'. t = 3.1875 Simplifying t = 3.1875Solution
t = {0, 3.1875}
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