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Simplifying 3t2 + 24t = -45 Reorder the terms: 24t + 3t2 = -45 Solving 24t + 3t2 = -45 Solving for variable 't'. Reorder the terms: 45 + 24t + 3t2 = -45 + 45 Combine like terms: -45 + 45 = 0 45 + 24t + 3t2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(15 + 8t + t2) = 0 Factor a trinomial. 3((5 + t)(3 + t)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(5 + t)' equal to zero and attempt to solve: Simplifying 5 + t = 0 Solving 5 + t = 0 Move all terms containing t to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + t = 0 + -5 Combine like terms: 5 + -5 = 0 0 + t = 0 + -5 t = 0 + -5 Combine like terms: 0 + -5 = -5 t = -5 Simplifying t = -5Subproblem 2
Set the factor '(3 + t)' equal to zero and attempt to solve: Simplifying 3 + t = 0 Solving 3 + t = 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 + t = 0 + -3 Combine like terms: 3 + -3 = 0 0 + t = 0 + -3 t = 0 + -3 Combine like terms: 0 + -3 = -3 t = -3 Simplifying t = -3Solution
t = {-5, -3}
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