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Simplifying 0 = 60 + 5t + -5t2 Solving 0 = 60 + 5t + -5t2 Solving for variable 't'. Combine like terms: 0 + -60 = -60 -60 + -5t + 5t2 = 60 + 5t + -5t2 + -60 + -5t + 5t2 Reorder the terms: -60 + -5t + 5t2 = 60 + -60 + 5t + -5t + -5t2 + 5t2 Combine like terms: 60 + -60 = 0 -60 + -5t + 5t2 = 0 + 5t + -5t + -5t2 + 5t2 -60 + -5t + 5t2 = 5t + -5t + -5t2 + 5t2 Combine like terms: 5t + -5t = 0 -60 + -5t + 5t2 = 0 + -5t2 + 5t2 -60 + -5t + 5t2 = -5t2 + 5t2 Combine like terms: -5t2 + 5t2 = 0 -60 + -5t + 5t2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-12 + -1t + t2) = 0 Factor a trinomial. 5((-3 + -1t)(4 + -1t)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-3 + -1t)' equal to zero and attempt to solve: Simplifying -3 + -1t = 0 Solving -3 + -1t = 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 + -1t = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1t = 0 + 3 -1t = 0 + 3 Combine like terms: 0 + 3 = 3 -1t = 3 Divide each side by '-1'. t = -3 Simplifying t = -3Subproblem 2
Set the factor '(4 + -1t)' equal to zero and attempt to solve: Simplifying 4 + -1t = 0 Solving 4 + -1t = 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 + -1t = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1t = 0 + -4 -1t = 0 + -4 Combine like terms: 0 + -4 = -4 -1t = -4 Divide each side by '-1'. t = 4 Simplifying t = 4Solution
t = {-3, 4}
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