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Simplifying 2t2 + 14t = -24 Reorder the terms: 14t + 2t2 = -24 Solving 14t + 2t2 = -24 Solving for variable 't'. Reorder the terms: 24 + 14t + 2t2 = -24 + 24 Combine like terms: -24 + 24 = 0 24 + 14t + 2t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(12 + 7t + t2) = 0 Factor a trinomial. 2((4 + t)(3 + t)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(4 + t)' equal to zero and attempt to solve: Simplifying 4 + t = 0 Solving 4 + t = 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 + t = 0 + -4 Combine like terms: 4 + -4 = 0 0 + t = 0 + -4 t = 0 + -4 Combine like terms: 0 + -4 = -4 t = -4 Simplifying t = -4Subproblem 2
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 = -3Solution
t = {-4, -3}
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