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Simplifying 0 = 3t2 + 2t + -1 Reorder the terms: 0 = -1 + 2t + 3t2 Solving 0 = -1 + 2t + 3t2 Solving for variable 't'. Combine like terms: 0 + 1 = 1 1 + -2t + -3t2 = -1 + 2t + 3t2 + 1 + -2t + -3t2 Reorder the terms: 1 + -2t + -3t2 = -1 + 1 + 2t + -2t + 3t2 + -3t2 Combine like terms: -1 + 1 = 0 1 + -2t + -3t2 = 0 + 2t + -2t + 3t2 + -3t2 1 + -2t + -3t2 = 2t + -2t + 3t2 + -3t2 Combine like terms: 2t + -2t = 0 1 + -2t + -3t2 = 0 + 3t2 + -3t2 1 + -2t + -3t2 = 3t2 + -3t2 Combine like terms: 3t2 + -3t2 = 0 1 + -2t + -3t2 = 0 Factor a trinomial. (1 + -3t)(1 + t) = 0Subproblem 1
Set the factor '(1 + -3t)' equal to zero and attempt to solve: Simplifying 1 + -3t = 0 Solving 1 + -3t = 0 Move all terms containing t to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -3t = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -3t = 0 + -1 -3t = 0 + -1 Combine like terms: 0 + -1 = -1 -3t = -1 Divide each side by '-3'. t = 0.3333333333 Simplifying t = 0.3333333333Subproblem 2
Set the factor '(1 + t)' equal to zero and attempt to solve: Simplifying 1 + t = 0 Solving 1 + t = 0 Move all terms containing t to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + t = 0 + -1 Combine like terms: 1 + -1 = 0 0 + t = 0 + -1 t = 0 + -1 Combine like terms: 0 + -1 = -1 t = -1 Simplifying t = -1Solution
t = {0.3333333333, -1}
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