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Simplifying 16t2 + 20t + -204 = 0 Reorder the terms: -204 + 20t + 16t2 = 0 Solving -204 + 20t + 16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '4'. 4(-51 + 5t + 4t2) = 0 Factor a trinomial. 4((-17 + -4t)(3 + -1t)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-17 + -4t)' equal to zero and attempt to solve: Simplifying -17 + -4t = 0 Solving -17 + -4t = 0 Move all terms containing t to the left, all other terms to the right. Add '17' to each side of the equation. -17 + 17 + -4t = 0 + 17 Combine like terms: -17 + 17 = 0 0 + -4t = 0 + 17 -4t = 0 + 17 Combine like terms: 0 + 17 = 17 -4t = 17 Divide each side by '-4'. t = -4.25 Simplifying t = -4.25Subproblem 2
Set the factor '(3 + -1t)' equal to zero and attempt to solve: Simplifying 3 + -1t = 0 Solving 3 + -1t = 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 + -1t = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1t = 0 + -3 -1t = 0 + -3 Combine like terms: 0 + -3 = -3 -1t = -3 Divide each side by '-1'. t = 3 Simplifying t = 3Solution
t = {-4.25, 3}
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