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Simplifying (3 + -5t)(7 + -8t) = 0 Multiply (3 + -5t) * (7 + -8t) (3(7 + -8t) + -5t * (7 + -8t)) = 0 ((7 * 3 + -8t * 3) + -5t * (7 + -8t)) = 0 ((21 + -24t) + -5t * (7 + -8t)) = 0 (21 + -24t + (7 * -5t + -8t * -5t)) = 0 (21 + -24t + (-35t + 40t2)) = 0 Combine like terms: -24t + -35t = -59t (21 + -59t + 40t2) = 0 Solving 21 + -59t + 40t2 = 0 Solving for variable 't'. Factor a trinomial. (3 + -5t)(7 + -8t) = 0Subproblem 1
Set the factor '(3 + -5t)' equal to zero and attempt to solve: Simplifying 3 + -5t = 0 Solving 3 + -5t = 0 Move all terms containing t to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -5t = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -5t = 0 + -3 -5t = 0 + -3 Combine like terms: 0 + -3 = -3 -5t = -3 Divide each side by '-5'. t = 0.6 Simplifying t = 0.6Subproblem 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 = {0.6, 0.875}
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