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Simplifying (7t + 5)(2t + -7) = 0 Reorder the terms: (5 + 7t)(2t + -7) = 0 Reorder the terms: (5 + 7t)(-7 + 2t) = 0 Multiply (5 + 7t) * (-7 + 2t) (5(-7 + 2t) + 7t * (-7 + 2t)) = 0 ((-7 * 5 + 2t * 5) + 7t * (-7 + 2t)) = 0 ((-35 + 10t) + 7t * (-7 + 2t)) = 0 (-35 + 10t + (-7 * 7t + 2t * 7t)) = 0 (-35 + 10t + (-49t + 14t2)) = 0 Combine like terms: 10t + -49t = -39t (-35 + -39t + 14t2) = 0 Solving -35 + -39t + 14t2 = 0 Solving for variable 't'. Factor a trinomial. (-5 + -7t)(7 + -2t) = 0Subproblem 1
Set the factor '(-5 + -7t)' equal to zero and attempt to solve: Simplifying -5 + -7t = 0 Solving -5 + -7t = 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 + -7t = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -7t = 0 + 5 -7t = 0 + 5 Combine like terms: 0 + 5 = 5 -7t = 5 Divide each side by '-7'. t = -0.7142857143 Simplifying t = -0.7142857143Subproblem 2
Set the factor '(7 + -2t)' equal to zero and attempt to solve: Simplifying 7 + -2t = 0 Solving 7 + -2t = 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 + -2t = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -2t = 0 + -7 -2t = 0 + -7 Combine like terms: 0 + -7 = -7 -2t = -7 Divide each side by '-2'. t = 3.5 Simplifying t = 3.5Solution
t = {-0.7142857143, 3.5}
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