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Simplifying (t + -1)(3t + -7) = 0 Reorder the terms: (-1 + t)(3t + -7) = 0 Reorder the terms: (-1 + t)(-7 + 3t) = 0 Multiply (-1 + t) * (-7 + 3t) (-1(-7 + 3t) + t(-7 + 3t)) = 0 ((-7 * -1 + 3t * -1) + t(-7 + 3t)) = 0 ((7 + -3t) + t(-7 + 3t)) = 0 (7 + -3t + (-7 * t + 3t * t)) = 0 (7 + -3t + (-7t + 3t2)) = 0 Combine like terms: -3t + -7t = -10t (7 + -10t + 3t2) = 0 Solving 7 + -10t + 3t2 = 0 Solving for variable 't'. Factor a trinomial. (1 + -1t)(7 + -3t) = 0Subproblem 1
Set the factor '(1 + -1t)' equal to zero and attempt to solve: Simplifying 1 + -1t = 0 Solving 1 + -1t = 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 + -1t = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1t = 0 + -1 -1t = 0 + -1 Combine like terms: 0 + -1 = -1 -1t = -1 Divide each side by '-1'. t = 1 Simplifying t = 1Subproblem 2
Set the factor '(7 + -3t)' equal to zero and attempt to solve: Simplifying 7 + -3t = 0 Solving 7 + -3t = 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 + -3t = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -3t = 0 + -7 -3t = 0 + -7 Combine like terms: 0 + -7 = -7 -3t = -7 Divide each side by '-3'. t = 2.333333333 Simplifying t = 2.333333333Solution
t = {1, 2.333333333}
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