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Simplifying (7t + 2)(5t + 9) = 0 Reorder the terms: (2 + 7t)(5t + 9) = 0 Reorder the terms: (2 + 7t)(9 + 5t) = 0 Multiply (2 + 7t) * (9 + 5t) (2(9 + 5t) + 7t * (9 + 5t)) = 0 ((9 * 2 + 5t * 2) + 7t * (9 + 5t)) = 0 ((18 + 10t) + 7t * (9 + 5t)) = 0 (18 + 10t + (9 * 7t + 5t * 7t)) = 0 (18 + 10t + (63t + 35t2)) = 0 Combine like terms: 10t + 63t = 73t (18 + 73t + 35t2) = 0 Solving 18 + 73t + 35t2 = 0 Solving for variable 't'. Factor a trinomial. (9 + 5t)(2 + 7t) = 0Subproblem 1
Set the factor '(9 + 5t)' equal to zero and attempt to solve: Simplifying 9 + 5t = 0 Solving 9 + 5t = 0 Move all terms containing t to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + 5t = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 5t = 0 + -9 5t = 0 + -9 Combine like terms: 0 + -9 = -9 5t = -9 Divide each side by '5'. t = -1.8 Simplifying t = -1.8Subproblem 2
Set the factor '(2 + 7t)' equal to zero and attempt to solve: Simplifying 2 + 7t = 0 Solving 2 + 7t = 0 Move all terms containing t to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + 7t = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 7t = 0 + -2 7t = 0 + -2 Combine like terms: 0 + -2 = -2 7t = -2 Divide each side by '7'. t = -0.2857142857 Simplifying t = -0.2857142857Solution
t = {-1.8, -0.2857142857}
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