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Simplifying 280 = -15t2 + 135t + 10 Reorder the terms: 280 = 10 + 135t + -15t2 Solving 280 = 10 + 135t + -15t2 Solving for variable 't'. Combine like terms: 280 + -10 = 270 270 + -135t + 15t2 = 10 + 135t + -15t2 + -10 + -135t + 15t2 Reorder the terms: 270 + -135t + 15t2 = 10 + -10 + 135t + -135t + -15t2 + 15t2 Combine like terms: 10 + -10 = 0 270 + -135t + 15t2 = 0 + 135t + -135t + -15t2 + 15t2 270 + -135t + 15t2 = 135t + -135t + -15t2 + 15t2 Combine like terms: 135t + -135t = 0 270 + -135t + 15t2 = 0 + -15t2 + 15t2 270 + -135t + 15t2 = -15t2 + 15t2 Combine like terms: -15t2 + 15t2 = 0 270 + -135t + 15t2 = 0 Factor out the Greatest Common Factor (GCF), '15'. 15(18 + -9t + t2) = 0 Factor a trinomial. 15((3 + -1t)(6 + -1t)) = 0 Ignore the factor 15.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 '(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 = {3, 6}
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