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Simplifying -16t2 + 132t + 108 = 0 Reorder the terms: 108 + 132t + -16t2 = 0 Solving 108 + 132t + -16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '4'. 4(27 + 33t + -4t2) = 0 Factor a trinomial. 4((9 + -1t)(3 + 4t)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(9 + -1t)' equal to zero and attempt to solve: Simplifying 9 + -1t = 0 Solving 9 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -1t = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1t = 0 + -9 -1t = 0 + -9 Combine like terms: 0 + -9 = -9 -1t = -9 Divide each side by '-1'. t = 9 Simplifying t = 9Subproblem 2
Set the factor '(3 + 4t)' equal to zero and attempt to solve: Simplifying 3 + 4t = 0 Solving 3 + 4t = 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 + 4t = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 4t = 0 + -3 4t = 0 + -3 Combine like terms: 0 + -3 = -3 4t = -3 Divide each side by '4'. t = -0.75 Simplifying t = -0.75Solution
t = {9, -0.75}
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