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Simplifying (7t + -3)(8t + -5) = 0 Reorder the terms: (-3 + 7t)(8t + -5) = 0 Reorder the terms: (-3 + 7t)(-5 + 8t) = 0 Multiply (-3 + 7t) * (-5 + 8t) (-3(-5 + 8t) + 7t * (-5 + 8t)) = 0 ((-5 * -3 + 8t * -3) + 7t * (-5 + 8t)) = 0 ((15 + -24t) + 7t * (-5 + 8t)) = 0 (15 + -24t + (-5 * 7t + 8t * 7t)) = 0 (15 + -24t + (-35t + 56t2)) = 0 Combine like terms: -24t + -35t = -59t (15 + -59t + 56t2) = 0 Solving 15 + -59t + 56t2 = 0 Solving for variable 't'. Factor a trinomial. (3 + -7t)(5 + -8t) = 0Subproblem 1
Set the factor '(3 + -7t)' equal to zero and attempt to solve: Simplifying 3 + -7t = 0 Solving 3 + -7t = 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 + -7t = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -7t = 0 + -3 -7t = 0 + -3 Combine like terms: 0 + -3 = -3 -7t = -3 Divide each side by '-7'. t = 0.4285714286 Simplifying t = 0.4285714286Subproblem 2
Set the factor '(5 + -8t)' equal to zero and attempt to solve: Simplifying 5 + -8t = 0 Solving 5 + -8t = 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 + -8t = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -8t = 0 + -5 -8t = 0 + -5 Combine like terms: 0 + -5 = -5 -8t = -5 Divide each side by '-8'. t = 0.625 Simplifying t = 0.625Solution
t = {0.4285714286, 0.625}
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