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Simplifying (3t + 4)(t + -7) = 0 Reorder the terms: (4 + 3t)(t + -7) = 0 Reorder the terms: (4 + 3t)(-7 + t) = 0 Multiply (4 + 3t) * (-7 + t) (4(-7 + t) + 3t * (-7 + t)) = 0 ((-7 * 4 + t * 4) + 3t * (-7 + t)) = 0 ((-28 + 4t) + 3t * (-7 + t)) = 0 (-28 + 4t + (-7 * 3t + t * 3t)) = 0 (-28 + 4t + (-21t + 3t2)) = 0 Combine like terms: 4t + -21t = -17t (-28 + -17t + 3t2) = 0 Solving -28 + -17t + 3t2 = 0 Solving for variable 't'. Factor a trinomial. (-4 + -3t)(7 + -1t) = 0Subproblem 1
Set the factor '(-4 + -3t)' equal to zero and attempt to solve: Simplifying -4 + -3t = 0 Solving -4 + -3t = 0 Move all terms containing t to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -3t = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -3t = 0 + 4 -3t = 0 + 4 Combine like terms: 0 + 4 = 4 -3t = 4 Divide each side by '-3'. t = -1.333333333 Simplifying t = -1.333333333Subproblem 2
Set the factor '(7 + -1t)' equal to zero and attempt to solve: Simplifying 7 + -1t = 0 Solving 7 + -1t = 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 + -1t = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1t = 0 + -7 -1t = 0 + -7 Combine like terms: 0 + -7 = -7 -1t = -7 Divide each side by '-1'. t = 7 Simplifying t = 7Solution
t = {-1.333333333, 7}
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