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Simplifying 0 = -16t2 + 288t + -1152 Reorder the terms: 0 = -1152 + 288t + -16t2 Solving 0 = -1152 + 288t + -16t2 Solving for variable 't'. Combine like terms: 0 + 1152 = 1152 1152 + -288t + 16t2 = -1152 + 288t + -16t2 + 1152 + -288t + 16t2 Reorder the terms: 1152 + -288t + 16t2 = -1152 + 1152 + 288t + -288t + -16t2 + 16t2 Combine like terms: -1152 + 1152 = 0 1152 + -288t + 16t2 = 0 + 288t + -288t + -16t2 + 16t2 1152 + -288t + 16t2 = 288t + -288t + -16t2 + 16t2 Combine like terms: 288t + -288t = 0 1152 + -288t + 16t2 = 0 + -16t2 + 16t2 1152 + -288t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 1152 + -288t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '16'. 16(72 + -18t + t2) = 0 Factor a trinomial. 16((6 + -1t)(12 + -1t)) = 0 Ignore the factor 16.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 '(12 + -1t)' equal to zero and attempt to solve: Simplifying 12 + -1t = 0 Solving 12 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + -1t = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -1t = 0 + -12 -1t = 0 + -12 Combine like terms: 0 + -12 = -12 -1t = -12 Divide each side by '-1'. t = 12 Simplifying t = 12Solution
t = {6, 12}
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