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Simplifying (7t + -1)(4t + 3) = 0 Reorder the terms: (-1 + 7t)(4t + 3) = 0 Reorder the terms: (-1 + 7t)(3 + 4t) = 0 Multiply (-1 + 7t) * (3 + 4t) (-1(3 + 4t) + 7t * (3 + 4t)) = 0 ((3 * -1 + 4t * -1) + 7t * (3 + 4t)) = 0 ((-3 + -4t) + 7t * (3 + 4t)) = 0 (-3 + -4t + (3 * 7t + 4t * 7t)) = 0 (-3 + -4t + (21t + 28t2)) = 0 Combine like terms: -4t + 21t = 17t (-3 + 17t + 28t2) = 0 Solving -3 + 17t + 28t2 = 0 Solving for variable 't'. Factor a trinomial. (-3 + -4t)(1 + -7t) = 0Subproblem 1
Set the factor '(-3 + -4t)' equal to zero and attempt to solve: Simplifying -3 + -4t = 0 Solving -3 + -4t = 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 + -4t = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -4t = 0 + 3 -4t = 0 + 3 Combine like terms: 0 + 3 = 3 -4t = 3 Divide each side by '-4'. t = -0.75 Simplifying t = -0.75Subproblem 2
Set the factor '(1 + -7t)' equal to zero and attempt to solve: Simplifying 1 + -7t = 0 Solving 1 + -7t = 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 + -7t = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -7t = 0 + -1 -7t = 0 + -1 Combine like terms: 0 + -1 = -1 -7t = -1 Divide each side by '-7'. t = 0.1428571429 Simplifying t = 0.1428571429Solution
t = {-0.75, 0.1428571429}
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