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Simplifying 0 = -16t2 + 32t + 48 Reorder the terms: 0 = 48 + 32t + -16t2 Solving 0 = 48 + 32t + -16t2 Solving for variable 't'. Combine like terms: 0 + -48 = -48 -48 + -32t + 16t2 = 48 + 32t + -16t2 + -48 + -32t + 16t2 Reorder the terms: -48 + -32t + 16t2 = 48 + -48 + 32t + -32t + -16t2 + 16t2 Combine like terms: 48 + -48 = 0 -48 + -32t + 16t2 = 0 + 32t + -32t + -16t2 + 16t2 -48 + -32t + 16t2 = 32t + -32t + -16t2 + 16t2 Combine like terms: 32t + -32t = 0 -48 + -32t + 16t2 = 0 + -16t2 + 16t2 -48 + -32t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -48 + -32t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '16'. 16(-3 + -2t + t2) = 0 Factor a trinomial. 16((-1 + -1t)(3 + -1t)) = 0 Ignore the factor 16.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 + -1t)' equal to zero and attempt to solve: Simplifying 3 + -1t = 0 Solving 3 + -1t = 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 + -1t = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1t = 0 + -3 -1t = 0 + -3 Combine like terms: 0 + -3 = -3 -1t = -3 Divide each side by '-1'. t = 3 Simplifying t = 3Solution
t = {-1, 3}
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