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Simplifying 6t2 + 26t + 24 = 0 Reorder the terms: 24 + 26t + 6t2 = 0 Solving 24 + 26t + 6t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '2'. 2(12 + 13t + 3t2) = 0 Factor a trinomial. 2((3 + t)(4 + 3t)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(3 + t)' equal to zero and attempt to solve: Simplifying 3 + t = 0 Solving 3 + t = 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 + t = 0 + -3 Combine like terms: 3 + -3 = 0 0 + t = 0 + -3 t = 0 + -3 Combine like terms: 0 + -3 = -3 t = -3 Simplifying t = -3Subproblem 2
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 = -1.333333333Solution
t = {-3, -1.333333333}
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