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Simplifying -16t2 + 240t + 864 = 0 Reorder the terms: 864 + 240t + -16t2 = 0 Solving 864 + 240t + -16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '16'. 16(54 + 15t + -1t2) = 0 Factor a trinomial. 16((18 + -1t)(3 + t)) = 0 Ignore the factor 16.Subproblem 1
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 = 18Subproblem 2
Set the factor '(3 + t)' equal to zero and attempt to solve: Simplifying 3 + t = 0 Solving 3 + t = 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 + t = 0 + -3 Combine like terms: 3 + -3 = 0 0 + t = 0 + -3 t = 0 + -3 Combine like terms: 0 + -3 = -3 t = -3 Simplifying t = -3Solution
t = {18, -3}
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