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Simplifying (2t + -7)(6t + 1) = 0 Reorder the terms: (-7 + 2t)(6t + 1) = 0 Reorder the terms: (-7 + 2t)(1 + 6t) = 0 Multiply (-7 + 2t) * (1 + 6t) (-7(1 + 6t) + 2t * (1 + 6t)) = 0 ((1 * -7 + 6t * -7) + 2t * (1 + 6t)) = 0 ((-7 + -42t) + 2t * (1 + 6t)) = 0 (-7 + -42t + (1 * 2t + 6t * 2t)) = 0 (-7 + -42t + (2t + 12t2)) = 0 Combine like terms: -42t + 2t = -40t (-7 + -40t + 12t2) = 0 Solving -7 + -40t + 12t2 = 0 Solving for variable 't'. Factor a trinomial. (-1 + -6t)(7 + -2t) = 0Subproblem 1
Set the factor '(-1 + -6t)' equal to zero and attempt to solve: Simplifying -1 + -6t = 0 Solving -1 + -6t = 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 + -6t = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -6t = 0 + 1 -6t = 0 + 1 Combine like terms: 0 + 1 = 1 -6t = 1 Divide each side by '-6'. t = -0.1666666667 Simplifying t = -0.1666666667Subproblem 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 = {-0.1666666667, 3.5}
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