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Simplifying (8t + 3)(4t + 7) = 0 Reorder the terms: (3 + 8t)(4t + 7) = 0 Reorder the terms: (3 + 8t)(7 + 4t) = 0 Multiply (3 + 8t) * (7 + 4t) (3(7 + 4t) + 8t * (7 + 4t)) = 0 ((7 * 3 + 4t * 3) + 8t * (7 + 4t)) = 0 ((21 + 12t) + 8t * (7 + 4t)) = 0 (21 + 12t + (7 * 8t + 4t * 8t)) = 0 (21 + 12t + (56t + 32t2)) = 0 Combine like terms: 12t + 56t = 68t (21 + 68t + 32t2) = 0 Solving 21 + 68t + 32t2 = 0 Solving for variable 't'. Factor a trinomial. (7 + 4t)(3 + 8t) = 0Subproblem 1
Set the factor '(7 + 4t)' equal to zero and attempt to solve: Simplifying 7 + 4t = 0 Solving 7 + 4t = 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 + 4t = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 4t = 0 + -7 4t = 0 + -7 Combine like terms: 0 + -7 = -7 4t = -7 Divide each side by '4'. t = -1.75 Simplifying t = -1.75Subproblem 2
Set the factor '(3 + 8t)' equal to zero and attempt to solve: Simplifying 3 + 8t = 0 Solving 3 + 8t = 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 + 8t = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 8t = 0 + -3 8t = 0 + -3 Combine like terms: 0 + -3 = -3 8t = -3 Divide each side by '8'. t = -0.375 Simplifying t = -0.375Solution
t = {-1.75, -0.375}
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