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Simplifying 0 = -15t2 + 150t + -315 Reorder the terms: 0 = -315 + 150t + -15t2 Solving 0 = -315 + 150t + -15t2 Solving for variable 't'. Combine like terms: 0 + 315 = 315 315 + -150t + 15t2 = -315 + 150t + -15t2 + 315 + -150t + 15t2 Reorder the terms: 315 + -150t + 15t2 = -315 + 315 + 150t + -150t + -15t2 + 15t2 Combine like terms: -315 + 315 = 0 315 + -150t + 15t2 = 0 + 150t + -150t + -15t2 + 15t2 315 + -150t + 15t2 = 150t + -150t + -15t2 + 15t2 Combine like terms: 150t + -150t = 0 315 + -150t + 15t2 = 0 + -15t2 + 15t2 315 + -150t + 15t2 = -15t2 + 15t2 Combine like terms: -15t2 + 15t2 = 0 315 + -150t + 15t2 = 0 Factor out the Greatest Common Factor (GCF), '15'. 15(21 + -10t + t2) = 0 Factor a trinomial. 15((3 + -1t)(7 + -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 '(7 + -1t)' equal to zero and attempt to solve: Simplifying 7 + -1t = 0 Solving 7 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1t = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1t = 0 + -7 -1t = 0 + -7 Combine like terms: 0 + -7 = -7 -1t = -7 Divide each side by '-1'. t = 7 Simplifying t = 7Solution
t = {3, 7}
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