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Simplifying 0 = 3t2 + -19t + -40 Reorder the terms: 0 = -40 + -19t + 3t2 Solving 0 = -40 + -19t + 3t2 Solving for variable 't'. Combine like terms: 0 + 40 = 40 40 + 19t + -3t2 = -40 + -19t + 3t2 + 40 + 19t + -3t2 Reorder the terms: 40 + 19t + -3t2 = -40 + 40 + -19t + 19t + 3t2 + -3t2 Combine like terms: -40 + 40 = 0 40 + 19t + -3t2 = 0 + -19t + 19t + 3t2 + -3t2 40 + 19t + -3t2 = -19t + 19t + 3t2 + -3t2 Combine like terms: -19t + 19t = 0 40 + 19t + -3t2 = 0 + 3t2 + -3t2 40 + 19t + -3t2 = 3t2 + -3t2 Combine like terms: 3t2 + -3t2 = 0 40 + 19t + -3t2 = 0 Factor a trinomial. (8 + -1t)(5 + 3t) = 0Subproblem 1
Set the factor '(8 + -1t)' equal to zero and attempt to solve: Simplifying 8 + -1t = 0 Solving 8 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1t = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1t = 0 + -8 -1t = 0 + -8 Combine like terms: 0 + -8 = -8 -1t = -8 Divide each side by '-1'. t = 8 Simplifying t = 8Subproblem 2
Set the factor '(5 + 3t)' equal to zero and attempt to solve: Simplifying 5 + 3t = 0 Solving 5 + 3t = 0 Move all terms containing t to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + 3t = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 3t = 0 + -5 3t = 0 + -5 Combine like terms: 0 + -5 = -5 3t = -5 Divide each side by '3'. t = -1.666666667 Simplifying t = -1.666666667Solution
t = {8, -1.666666667}
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