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Simplifying (2t + 1)(5t + 7) = 0 Reorder the terms: (1 + 2t)(5t + 7) = 0 Reorder the terms: (1 + 2t)(7 + 5t) = 0 Multiply (1 + 2t) * (7 + 5t) (1(7 + 5t) + 2t * (7 + 5t)) = 0 ((7 * 1 + 5t * 1) + 2t * (7 + 5t)) = 0 ((7 + 5t) + 2t * (7 + 5t)) = 0 (7 + 5t + (7 * 2t + 5t * 2t)) = 0 (7 + 5t + (14t + 10t2)) = 0 Combine like terms: 5t + 14t = 19t (7 + 19t + 10t2) = 0 Solving 7 + 19t + 10t2 = 0 Solving for variable 't'. Factor a trinomial. (7 + 5t)(1 + 2t) = 0Subproblem 1
Set the factor '(7 + 5t)' equal to zero and attempt to solve: Simplifying 7 + 5t = 0 Solving 7 + 5t = 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 + 5t = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 5t = 0 + -7 5t = 0 + -7 Combine like terms: 0 + -7 = -7 5t = -7 Divide each side by '5'. t = -1.4 Simplifying t = -1.4Subproblem 2
Set the factor '(1 + 2t)' equal to zero and attempt to solve: Simplifying 1 + 2t = 0 Solving 1 + 2t = 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 + 2t = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2t = 0 + -1 2t = 0 + -1 Combine like terms: 0 + -1 = -1 2t = -1 Divide each side by '2'. t = -0.5 Simplifying t = -0.5Solution
t = {-1.4, -0.5}
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