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Simplifying (9t + 7)(4t + 5) = 0 Reorder the terms: (7 + 9t)(4t + 5) = 0 Reorder the terms: (7 + 9t)(5 + 4t) = 0 Multiply (7 + 9t) * (5 + 4t) (7(5 + 4t) + 9t * (5 + 4t)) = 0 ((5 * 7 + 4t * 7) + 9t * (5 + 4t)) = 0 ((35 + 28t) + 9t * (5 + 4t)) = 0 (35 + 28t + (5 * 9t + 4t * 9t)) = 0 (35 + 28t + (45t + 36t2)) = 0 Combine like terms: 28t + 45t = 73t (35 + 73t + 36t2) = 0 Solving 35 + 73t + 36t2 = 0 Solving for variable 't'. Factor a trinomial. (5 + 4t)(7 + 9t) = 0Subproblem 1
Set the factor '(5 + 4t)' equal to zero and attempt to solve: Simplifying 5 + 4t = 0 Solving 5 + 4t = 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 + 4t = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 4t = 0 + -5 4t = 0 + -5 Combine like terms: 0 + -5 = -5 4t = -5 Divide each side by '4'. t = -1.25 Simplifying t = -1.25Subproblem 2
Set the factor '(7 + 9t)' equal to zero and attempt to solve: Simplifying 7 + 9t = 0 Solving 7 + 9t = 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 + 9t = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 9t = 0 + -7 9t = 0 + -7 Combine like terms: 0 + -7 = -7 9t = -7 Divide each side by '9'. t = -0.7777777778 Simplifying t = -0.7777777778Solution
t = {-1.25, -0.7777777778}
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