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Simplifying 0 = -16t2 + 128t + -112 Reorder the terms: 0 = -112 + 128t + -16t2 Solving 0 = -112 + 128t + -16t2 Solving for variable 't'. Combine like terms: 0 + 112 = 112 112 + -128t + 16t2 = -112 + 128t + -16t2 + 112 + -128t + 16t2 Reorder the terms: 112 + -128t + 16t2 = -112 + 112 + 128t + -128t + -16t2 + 16t2 Combine like terms: -112 + 112 = 0 112 + -128t + 16t2 = 0 + 128t + -128t + -16t2 + 16t2 112 + -128t + 16t2 = 128t + -128t + -16t2 + 16t2 Combine like terms: 128t + -128t = 0 112 + -128t + 16t2 = 0 + -16t2 + 16t2 112 + -128t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 112 + -128t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '16'. 16(7 + -8t + t2) = 0 Factor a trinomial. 16((1 + -1t)(7 + -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 '(7 + -1t)' equal to zero and attempt to solve: Simplifying 7 + -1t = 0 Solving 7 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1t = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1t = 0 + -7 -1t = 0 + -7 Combine like terms: 0 + -7 = -7 -1t = -7 Divide each side by '-1'. t = 7 Simplifying t = 7Solution
t = {1, 7}
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