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Simplifying (7t + -1t + -7)(3t + 7t + -1) = 0 Reorder the terms: (-7 + 7t + -1t)(3t + 7t + -1) = 0 Combine like terms: 7t + -1t = 6t (-7 + 6t)(3t + 7t + -1) = 0 Reorder the terms: (-7 + 6t)(-1 + 3t + 7t) = 0 Combine like terms: 3t + 7t = 10t (-7 + 6t)(-1 + 10t) = 0 Multiply (-7 + 6t) * (-1 + 10t) (-7(-1 + 10t) + 6t * (-1 + 10t)) = 0 ((-1 * -7 + 10t * -7) + 6t * (-1 + 10t)) = 0 ((7 + -70t) + 6t * (-1 + 10t)) = 0 (7 + -70t + (-1 * 6t + 10t * 6t)) = 0 (7 + -70t + (-6t + 60t2)) = 0 Combine like terms: -70t + -6t = -76t (7 + -76t + 60t2) = 0 Solving 7 + -76t + 60t2 = 0 Solving for variable 't'. Factor a trinomial. (1 + -10t)(7 + -6t) = 0Subproblem 1
Set the factor '(1 + -10t)' equal to zero and attempt to solve: Simplifying 1 + -10t = 0 Solving 1 + -10t = 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 + -10t = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -10t = 0 + -1 -10t = 0 + -1 Combine like terms: 0 + -1 = -1 -10t = -1 Divide each side by '-10'. t = 0.1 Simplifying t = 0.1Subproblem 2
Set the factor '(7 + -6t)' equal to zero and attempt to solve: Simplifying 7 + -6t = 0 Solving 7 + -6t = 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 + -6t = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -6t = 0 + -7 -6t = 0 + -7 Combine like terms: 0 + -7 = -7 -6t = -7 Divide each side by '-6'. t = 1.166666667 Simplifying t = 1.166666667Solution
t = {0.1, 1.166666667}
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