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Simplifying 0 = -16t2 + 48t + 864 Reorder the terms: 0 = 864 + 48t + -16t2 Solving 0 = 864 + 48t + -16t2 Solving for variable 't'. Combine like terms: 0 + -864 = -864 -864 + -48t + 16t2 = 864 + 48t + -16t2 + -864 + -48t + 16t2 Reorder the terms: -864 + -48t + 16t2 = 864 + -864 + 48t + -48t + -16t2 + 16t2 Combine like terms: 864 + -864 = 0 -864 + -48t + 16t2 = 0 + 48t + -48t + -16t2 + 16t2 -864 + -48t + 16t2 = 48t + -48t + -16t2 + 16t2 Combine like terms: 48t + -48t = 0 -864 + -48t + 16t2 = 0 + -16t2 + 16t2 -864 + -48t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -864 + -48t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '16'. 16(-54 + -3t + t2) = 0 Factor a trinomial. 16((-6 + -1t)(9 + -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 '(9 + -1t)' equal to zero and attempt to solve: Simplifying 9 + -1t = 0 Solving 9 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -1t = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1t = 0 + -9 -1t = 0 + -9 Combine like terms: 0 + -9 = -9 -1t = -9 Divide each side by '-1'. t = 9 Simplifying t = 9Solution
t = {-6, 9}
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