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Simplifying 190 = -15t2 + 120t + 10 Reorder the terms: 190 = 10 + 120t + -15t2 Solving 190 = 10 + 120t + -15t2 Solving for variable 't'. Combine like terms: 190 + -10 = 180 180 + -120t + 15t2 = 10 + 120t + -15t2 + -10 + -120t + 15t2 Reorder the terms: 180 + -120t + 15t2 = 10 + -10 + 120t + -120t + -15t2 + 15t2 Combine like terms: 10 + -10 = 0 180 + -120t + 15t2 = 0 + 120t + -120t + -15t2 + 15t2 180 + -120t + 15t2 = 120t + -120t + -15t2 + 15t2 Combine like terms: 120t + -120t = 0 180 + -120t + 15t2 = 0 + -15t2 + 15t2 180 + -120t + 15t2 = -15t2 + 15t2 Combine like terms: -15t2 + 15t2 = 0 180 + -120t + 15t2 = 0 Factor out the Greatest Common Factor (GCF), '15'. 15(12 + -8t + t2) = 0 Factor a trinomial. 15((2 + -1t)(6 + -1t)) = 0 Ignore the factor 15.Subproblem 1
Set the factor '(2 + -1t)' equal to zero and attempt to solve: Simplifying 2 + -1t = 0 Solving 2 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1t = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1t = 0 + -2 -1t = 0 + -2 Combine like terms: 0 + -2 = -2 -1t = -2 Divide each side by '-1'. t = 2 Simplifying t = 2Subproblem 2
Set the factor '(6 + -1t)' equal to zero and attempt to solve: Simplifying 6 + -1t = 0 Solving 6 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1t = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1t = 0 + -6 -1t = 0 + -6 Combine like terms: 0 + -6 = -6 -1t = -6 Divide each side by '-1'. t = 6 Simplifying t = 6Solution
t = {2, 6}
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