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Simplifying (14t + 9)(5t + 5) = 0 Reorder the terms: (9 + 14t)(5t + 5) = 0 Reorder the terms: (9 + 14t)(5 + 5t) = 0 Multiply (9 + 14t) * (5 + 5t) (9(5 + 5t) + 14t * (5 + 5t)) = 0 ((5 * 9 + 5t * 9) + 14t * (5 + 5t)) = 0 ((45 + 45t) + 14t * (5 + 5t)) = 0 (45 + 45t + (5 * 14t + 5t * 14t)) = 0 (45 + 45t + (70t + 70t2)) = 0 Combine like terms: 45t + 70t = 115t (45 + 115t + 70t2) = 0 Solving 45 + 115t + 70t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '5'. 5(9 + 23t + 14t2) = 0 Factor a trinomial. 5((1 + t)(9 + 14t)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(1 + t)' equal to zero and attempt to solve: Simplifying 1 + t = 0 Solving 1 + t = 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 + t = 0 + -1 Combine like terms: 1 + -1 = 0 0 + t = 0 + -1 t = 0 + -1 Combine like terms: 0 + -1 = -1 t = -1 Simplifying t = -1Subproblem 2
Set the factor '(9 + 14t)' equal to zero and attempt to solve: Simplifying 9 + 14t = 0 Solving 9 + 14t = 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 + 14t = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 14t = 0 + -9 14t = 0 + -9 Combine like terms: 0 + -9 = -9 14t = -9 Divide each side by '14'. t = -0.6428571429 Simplifying t = -0.6428571429Solution
t = {-1, -0.6428571429}
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