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Simplifying 5 = 3t2 + -9t + -7 Reorder the terms: 5 = -7 + -9t + 3t2 Solving 5 = -7 + -9t + 3t2 Solving for variable 't'. Combine like terms: 5 + 7 = 12 12 + 9t + -3t2 = -7 + -9t + 3t2 + 7 + 9t + -3t2 Reorder the terms: 12 + 9t + -3t2 = -7 + 7 + -9t + 9t + 3t2 + -3t2 Combine like terms: -7 + 7 = 0 12 + 9t + -3t2 = 0 + -9t + 9t + 3t2 + -3t2 12 + 9t + -3t2 = -9t + 9t + 3t2 + -3t2 Combine like terms: -9t + 9t = 0 12 + 9t + -3t2 = 0 + 3t2 + -3t2 12 + 9t + -3t2 = 3t2 + -3t2 Combine like terms: 3t2 + -3t2 = 0 12 + 9t + -3t2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(4 + 3t + -1t2) = 0 Factor a trinomial. 3((4 + -1t)(1 + t)) = 0 Ignore the factor 3.Subproblem 1
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 = 4Subproblem 2
Set the factor '(1 + t)' equal to zero and attempt to solve: Simplifying 1 + t = 0 Solving 1 + t = 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 + t = 0 + -1 Combine like terms: 1 + -1 = 0 0 + t = 0 + -1 t = 0 + -1 Combine like terms: 0 + -1 = -1 t = -1 Simplifying t = -1Solution
t = {4, -1}
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