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Simplifying -16t2 + 128t + 768 = 0 Reorder the terms: 768 + 128t + -16t2 = 0 Solving 768 + 128t + -16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '16'. 16(48 + 8t + -1t2) = 0 Factor a trinomial. 16((12 + -1t)(4 + t)) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(12 + -1t)' equal to zero and attempt to solve: Simplifying 12 + -1t = 0 Solving 12 + -1t = 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 + -1t = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -1t = 0 + -12 -1t = 0 + -12 Combine like terms: 0 + -12 = -12 -1t = -12 Divide each side by '-1'. t = 12 Simplifying t = 12Subproblem 2
Set the factor '(4 + t)' equal to zero and attempt to solve: Simplifying 4 + t = 0 Solving 4 + t = 0 Move all terms containing t to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + t = 0 + -4 Combine like terms: 4 + -4 = 0 0 + t = 0 + -4 t = 0 + -4 Combine like terms: 0 + -4 = -4 t = -4 Simplifying t = -4Solution
t = {12, -4}
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