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Simplifying 8t2 + 32t + 24 = 0 Reorder the terms: 24 + 32t + 8t2 = 0 Solving 24 + 32t + 8t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '8'. 8(3 + 4t + t2) = 0 Factor a trinomial. 8((3 + t)(1 + t)) = 0 Ignore the factor 8.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 '(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 = {-3, -1}
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