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Simplifying -16t2 + 60t = 54 Reorder the terms: 60t + -16t2 = 54 Solving 60t + -16t2 = 54 Solving for variable 't'. Reorder the terms: -54 + 60t + -16t2 = 54 + -54 Combine like terms: 54 + -54 = 0 -54 + 60t + -16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-27 + 30t + -8t2) = 0 Factor a trinomial. 2((-9 + 4t)(3 + -2t)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-9 + 4t)' equal to zero and attempt to solve: Simplifying -9 + 4t = 0 Solving -9 + 4t = 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 + 4t = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 4t = 0 + 9 4t = 0 + 9 Combine like terms: 0 + 9 = 9 4t = 9 Divide each side by '4'. t = 2.25 Simplifying t = 2.25Subproblem 2
Set the factor '(3 + -2t)' equal to zero and attempt to solve: Simplifying 3 + -2t = 0 Solving 3 + -2t = 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 + -2t = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2t = 0 + -3 -2t = 0 + -3 Combine like terms: 0 + -3 = -3 -2t = -3 Divide each side by '-2'. t = 1.5 Simplifying t = 1.5Solution
t = {2.25, 1.5}
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