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Simplifying 32t2 + 24t + 80t + 60 = 0 Reorder the terms: 60 + 24t + 80t + 32t2 = 0 Combine like terms: 24t + 80t = 104t 60 + 104t + 32t2 = 0 Solving 60 + 104t + 32t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '4'. 4(15 + 26t + 8t2) = 0 Factor a trinomial. 4((5 + 2t)(3 + 4t)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(5 + 2t)' equal to zero and attempt to solve: Simplifying 5 + 2t = 0 Solving 5 + 2t = 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 + 2t = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 2t = 0 + -5 2t = 0 + -5 Combine like terms: 0 + -5 = -5 2t = -5 Divide each side by '2'. t = -2.5 Simplifying t = -2.5Subproblem 2
Set the factor '(3 + 4t)' equal to zero and attempt to solve: Simplifying 3 + 4t = 0 Solving 3 + 4t = 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 + 4t = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 4t = 0 + -3 4t = 0 + -3 Combine like terms: 0 + -3 = -3 4t = -3 Divide each side by '4'. t = -0.75 Simplifying t = -0.75Solution
t = {-2.5, -0.75}
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