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Simplifying 27t2 + 72t + 48 = 0 Reorder the terms: 48 + 72t + 27t2 = 0 Solving 48 + 72t + 27t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '3'. 3(16 + 24t + 9t2) = 0 Factor a trinomial. 3((4 + 3t)(4 + 3t)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(4 + 3t)' equal to zero and attempt to solve: Simplifying 4 + 3t = 0 Solving 4 + 3t = 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 + 3t = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 3t = 0 + -4 3t = 0 + -4 Combine like terms: 0 + -4 = -4 3t = -4 Divide each side by '3'. t = -1.333333333 Simplifying t = -1.333333333Subproblem 2
Set the factor '(4 + 3t)' equal to zero and attempt to solve: Simplifying 4 + 3t = 0 Solving 4 + 3t = 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 + 3t = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 3t = 0 + -4 3t = 0 + -4 Combine like terms: 0 + -4 = -4 3t = -4 Divide each side by '3'. t = -1.333333333 Simplifying t = -1.333333333Solution
t = {-1.333333333, -1.333333333}
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