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Simplifying 3t2 + -42t = -120 Reorder the terms: -42t + 3t2 = -120 Solving -42t + 3t2 = -120 Solving for variable 't'. Reorder the terms: 120 + -42t + 3t2 = -120 + 120 Combine like terms: -120 + 120 = 0 120 + -42t + 3t2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(40 + -14t + t2) = 0 Factor a trinomial. 3((4 + -1t)(10 + -1t)) = 0 Ignore the factor 3.Subproblem 1
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 = 4Subproblem 2
Set the factor '(10 + -1t)' equal to zero and attempt to solve: Simplifying 10 + -1t = 0 Solving 10 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + -1t = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -1t = 0 + -10 -1t = 0 + -10 Combine like terms: 0 + -10 = -10 -1t = -10 Divide each side by '-1'. t = 10 Simplifying t = 10Solution
t = {4, 10}
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