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Simplifying 3(t + 7)(t + -4) = 0 Reorder the terms: 3(7 + t)(t + -4) = 0 Reorder the terms: 3(7 + t)(-4 + t) = 0 Multiply (7 + t) * (-4 + t) 3(7(-4 + t) + t(-4 + t)) = 0 3((-4 * 7 + t * 7) + t(-4 + t)) = 0 3((-28 + 7t) + t(-4 + t)) = 0 3(-28 + 7t + (-4 * t + t * t)) = 0 3(-28 + 7t + (-4t + t2)) = 0 Combine like terms: 7t + -4t = 3t 3(-28 + 3t + t2) = 0 (-28 * 3 + 3t * 3 + t2 * 3) = 0 (-84 + 9t + 3t2) = 0 Solving -84 + 9t + 3t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '3'. 3(-28 + 3t + t2) = 0 Factor a trinomial. 3((-7 + -1t)(4 + -1t)) = 0 Ignore the factor 3.Subproblem 1
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 = -7Subproblem 2
Set the factor '(4 + -1t)' equal to zero and attempt to solve: Simplifying 4 + -1t = 0 Solving 4 + -1t = 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 + -1t = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1t = 0 + -4 -1t = 0 + -4 Combine like terms: 0 + -4 = -4 -1t = -4 Divide each side by '-1'. t = 4 Simplifying t = 4Solution
t = {-7, 4}
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