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Simplifying (7t + 5)(2t + -6) = 0 Reorder the terms: (5 + 7t)(2t + -6) = 0 Reorder the terms: (5 + 7t)(-6 + 2t) = 0 Multiply (5 + 7t) * (-6 + 2t) (5(-6 + 2t) + 7t * (-6 + 2t)) = 0 ((-6 * 5 + 2t * 5) + 7t * (-6 + 2t)) = 0 ((-30 + 10t) + 7t * (-6 + 2t)) = 0 (-30 + 10t + (-6 * 7t + 2t * 7t)) = 0 (-30 + 10t + (-42t + 14t2)) = 0 Combine like terms: 10t + -42t = -32t (-30 + -32t + 14t2) = 0 Solving -30 + -32t + 14t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '2'. 2(-15 + -16t + 7t2) = 0 Factor a trinomial. 2((-5 + -7t)(3 + -1t)) = 0 Ignore the factor 2.Subproblem 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 '(3 + -1t)' equal to zero and attempt to solve: Simplifying 3 + -1t = 0 Solving 3 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1t = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1t = 0 + -3 -1t = 0 + -3 Combine like terms: 0 + -3 = -3 -1t = -3 Divide each side by '-1'. t = 3 Simplifying t = 3Solution
t = {-0.7142857143, 3}
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