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Simplifying -16t2 + 96t + 192 = 272t Reorder the terms: 192 + 96t + -16t2 = 272t Solving 192 + 96t + -16t2 = 272t Solving for variable 't'. Reorder the terms: 192 + 96t + -272t + -16t2 = 272t + -272t Combine like terms: 96t + -272t = -176t 192 + -176t + -16t2 = 272t + -272t Combine like terms: 272t + -272t = 0 192 + -176t + -16t2 = 0 Factor out the Greatest Common Factor (GCF), '16'. 16(12 + -11t + -1t2) = 0 Factor a trinomial. 16((1 + -1t)(12 + t)) = 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 '(12 + t)' equal to zero and attempt to solve: Simplifying 12 + t = 0 Solving 12 + t = 0 Move all terms containing t to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + t = 0 + -12 Combine like terms: 12 + -12 = 0 0 + t = 0 + -12 t = 0 + -12 Combine like terms: 0 + -12 = -12 t = -12 Simplifying t = -12Solution
t = {1, -12}
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