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Simplifying 0 = 3t2 + 12t + -96 Reorder the terms: 0 = -96 + 12t + 3t2 Solving 0 = -96 + 12t + 3t2 Solving for variable 't'. Combine like terms: 0 + 96 = 96 96 + -12t + -3t2 = -96 + 12t + 3t2 + 96 + -12t + -3t2 Reorder the terms: 96 + -12t + -3t2 = -96 + 96 + 12t + -12t + 3t2 + -3t2 Combine like terms: -96 + 96 = 0 96 + -12t + -3t2 = 0 + 12t + -12t + 3t2 + -3t2 96 + -12t + -3t2 = 12t + -12t + 3t2 + -3t2 Combine like terms: 12t + -12t = 0 96 + -12t + -3t2 = 0 + 3t2 + -3t2 96 + -12t + -3t2 = 3t2 + -3t2 Combine like terms: 3t2 + -3t2 = 0 96 + -12t + -3t2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(32 + -4t + -1t2) = 0 Factor a trinomial. 3((4 + -1t)(8 + 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 '(8 + t)' equal to zero and attempt to solve: Simplifying 8 + t = 0 Solving 8 + t = 0 Move all terms containing t to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + t = 0 + -8 Combine like terms: 8 + -8 = 0 0 + t = 0 + -8 t = 0 + -8 Combine like terms: 0 + -8 = -8 t = -8 Simplifying t = -8Solution
t = {4, -8}
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