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Simplifying 0 = -5t2 + 20t + -15 Reorder the terms: 0 = -15 + 20t + -5t2 Solving 0 = -15 + 20t + -5t2 Solving for variable 't'. Combine like terms: 0 + 15 = 15 15 + -20t + 5t2 = -15 + 20t + -5t2 + 15 + -20t + 5t2 Reorder the terms: 15 + -20t + 5t2 = -15 + 15 + 20t + -20t + -5t2 + 5t2 Combine like terms: -15 + 15 = 0 15 + -20t + 5t2 = 0 + 20t + -20t + -5t2 + 5t2 15 + -20t + 5t2 = 20t + -20t + -5t2 + 5t2 Combine like terms: 20t + -20t = 0 15 + -20t + 5t2 = 0 + -5t2 + 5t2 15 + -20t + 5t2 = -5t2 + 5t2 Combine like terms: -5t2 + 5t2 = 0 15 + -20t + 5t2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(3 + -4t + t2) = 0 Factor a trinomial. 5((1 + -1t)(3 + -1t)) = 0 Ignore the factor 5.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 '(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 = 3Solution
t = {1, 3}
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