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Simplifying 3t(t + -7) = 54 Reorder the terms: 3t(-7 + t) = 54 (-7 * 3t + t * 3t) = 54 (-21t + 3t2) = 54 Solving -21t + 3t2 = 54 Solving for variable 't'. Reorder the terms: -54 + -21t + 3t2 = 54 + -54 Combine like terms: 54 + -54 = 0 -54 + -21t + 3t2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-18 + -7t + t2) = 0 Factor a trinomial. 3((-2 + -1t)(9 + -1t)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-2 + -1t)' equal to zero and attempt to solve: Simplifying -2 + -1t = 0 Solving -2 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -1t = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1t = 0 + 2 -1t = 0 + 2 Combine like terms: 0 + 2 = 2 -1t = 2 Divide each side by '-1'. t = -2 Simplifying t = -2Subproblem 2
Set the factor '(9 + -1t)' equal to zero and attempt to solve: Simplifying 9 + -1t = 0 Solving 9 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -1t = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1t = 0 + -9 -1t = 0 + -9 Combine like terms: 0 + -9 = -9 -1t = -9 Divide each side by '-1'. t = 9 Simplifying t = 9Solution
t = {-2, 9}
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