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Simplifying 0 = -16t2 + 32t + 768 Reorder the terms: 0 = 768 + 32t + -16t2 Solving 0 = 768 + 32t + -16t2 Solving for variable 't'. Combine like terms: 0 + -768 = -768 -768 + -32t + 16t2 = 768 + 32t + -16t2 + -768 + -32t + 16t2 Reorder the terms: -768 + -32t + 16t2 = 768 + -768 + 32t + -32t + -16t2 + 16t2 Combine like terms: 768 + -768 = 0 -768 + -32t + 16t2 = 0 + 32t + -32t + -16t2 + 16t2 -768 + -32t + 16t2 = 32t + -32t + -16t2 + 16t2 Combine like terms: 32t + -32t = 0 -768 + -32t + 16t2 = 0 + -16t2 + 16t2 -768 + -32t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -768 + -32t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '16'. 16(-48 + -2t + t2) = 0 Factor a trinomial. 16((-6 + -1t)(8 + -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 '(8 + -1t)' equal to zero and attempt to solve: Simplifying 8 + -1t = 0 Solving 8 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1t = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1t = 0 + -8 -1t = 0 + -8 Combine like terms: 0 + -8 = -8 -1t = -8 Divide each side by '-1'. t = 8 Simplifying t = 8Solution
t = {-6, 8}
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