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Simplifying (8t + -7)(3t + 5) = 0 Reorder the terms: (-7 + 8t)(3t + 5) = 0 Reorder the terms: (-7 + 8t)(5 + 3t) = 0 Multiply (-7 + 8t) * (5 + 3t) (-7(5 + 3t) + 8t * (5 + 3t)) = 0 ((5 * -7 + 3t * -7) + 8t * (5 + 3t)) = 0 ((-35 + -21t) + 8t * (5 + 3t)) = 0 (-35 + -21t + (5 * 8t + 3t * 8t)) = 0 (-35 + -21t + (40t + 24t2)) = 0 Combine like terms: -21t + 40t = 19t (-35 + 19t + 24t2) = 0 Solving -35 + 19t + 24t2 = 0 Solving for variable 't'. Factor a trinomial. (-5 + -3t)(7 + -8t) = 0Subproblem 1
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 = -1.666666667Subproblem 2
Set the factor '(7 + -8t)' equal to zero and attempt to solve: Simplifying 7 + -8t = 0 Solving 7 + -8t = 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 + -8t = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -8t = 0 + -7 -8t = 0 + -7 Combine like terms: 0 + -7 = -7 -8t = -7 Divide each side by '-8'. t = 0.875 Simplifying t = 0.875Solution
t = {-1.666666667, 0.875}
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