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Simplifying 3t2 + -78t + 480 = 0 Reorder the terms: 480 + -78t + 3t2 = 0 Solving 480 + -78t + 3t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '3'. 3(160 + -26t + t2) = 0 Factor a trinomial. 3((10 + -1t)(16 + -1t)) = 0 Ignore the factor 3.Subproblem 1
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 = 10Subproblem 2
Set the factor '(16 + -1t)' equal to zero and attempt to solve: Simplifying 16 + -1t = 0 Solving 16 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-16' to each side of the equation. 16 + -16 + -1t = 0 + -16 Combine like terms: 16 + -16 = 0 0 + -1t = 0 + -16 -1t = 0 + -16 Combine like terms: 0 + -16 = -16 -1t = -16 Divide each side by '-1'. t = 16 Simplifying t = 16Solution
t = {10, 16}
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