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Simplifying 0 = 18t + -3t2 + -15 Reorder the terms: 0 = -15 + 18t + -3t2 Solving 0 = -15 + 18t + -3t2 Solving for variable 't'. Combine like terms: 0 + 15 = 15 15 + -18t + 3t2 = -15 + 18t + -3t2 + 15 + -18t + 3t2 Reorder the terms: 15 + -18t + 3t2 = -15 + 15 + 18t + -18t + -3t2 + 3t2 Combine like terms: -15 + 15 = 0 15 + -18t + 3t2 = 0 + 18t + -18t + -3t2 + 3t2 15 + -18t + 3t2 = 18t + -18t + -3t2 + 3t2 Combine like terms: 18t + -18t = 0 15 + -18t + 3t2 = 0 + -3t2 + 3t2 15 + -18t + 3t2 = -3t2 + 3t2 Combine like terms: -3t2 + 3t2 = 0 15 + -18t + 3t2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(5 + -6t + t2) = 0 Factor a trinomial. 3((1 + -1t)(5 + -1t)) = 0 Ignore the factor 3.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 '(5 + -1t)' equal to zero and attempt to solve: Simplifying 5 + -1t = 0 Solving 5 + -1t = 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 + -1t = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1t = 0 + -5 -1t = 0 + -5 Combine like terms: 0 + -5 = -5 -1t = -5 Divide each side by '-1'. t = 5 Simplifying t = 5Solution
t = {1, 5}
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