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Simplifying 0 = -16t2 + 8t + 24 Reorder the terms: 0 = 24 + 8t + -16t2 Solving 0 = 24 + 8t + -16t2 Solving for variable 't'. Combine like terms: 0 + -24 = -24 -24 + -8t + 16t2 = 24 + 8t + -16t2 + -24 + -8t + 16t2 Reorder the terms: -24 + -8t + 16t2 = 24 + -24 + 8t + -8t + -16t2 + 16t2 Combine like terms: 24 + -24 = 0 -24 + -8t + 16t2 = 0 + 8t + -8t + -16t2 + 16t2 -24 + -8t + 16t2 = 8t + -8t + -16t2 + 16t2 Combine like terms: 8t + -8t = 0 -24 + -8t + 16t2 = 0 + -16t2 + 16t2 -24 + -8t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -24 + -8t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '8'. 8(-3 + -1t + 2t2) = 0 Factor a trinomial. 8((-1 + -1t)(3 + -2t)) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(-1 + -1t)' equal to zero and attempt to solve: Simplifying -1 + -1t = 0 Solving -1 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -1t = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1t = 0 + 1 -1t = 0 + 1 Combine like terms: 0 + 1 = 1 -1t = 1 Divide each side by '-1'. t = -1 Simplifying t = -1Subproblem 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 = {-1, 1.5}
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