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Simplifying 0 = -16t2 + 72t + -45 Reorder the terms: 0 = -45 + 72t + -16t2 Solving 0 = -45 + 72t + -16t2 Solving for variable 't'. Combine like terms: 0 + 45 = 45 45 + -72t + 16t2 = -45 + 72t + -16t2 + 45 + -72t + 16t2 Reorder the terms: 45 + -72t + 16t2 = -45 + 45 + 72t + -72t + -16t2 + 16t2 Combine like terms: -45 + 45 = 0 45 + -72t + 16t2 = 0 + 72t + -72t + -16t2 + 16t2 45 + -72t + 16t2 = 72t + -72t + -16t2 + 16t2 Combine like terms: 72t + -72t = 0 45 + -72t + 16t2 = 0 + -16t2 + 16t2 45 + -72t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 45 + -72t + 16t2 = 0 Factor a trinomial. (3 + -4t)(15 + -4t) = 0Subproblem 1
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 = 0.75Subproblem 2
Set the factor '(15 + -4t)' equal to zero and attempt to solve: Simplifying 15 + -4t = 0 Solving 15 + -4t = 0 Move all terms containing t to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + -4t = 0 + -15 Combine like terms: 15 + -15 = 0 0 + -4t = 0 + -15 -4t = 0 + -15 Combine like terms: 0 + -15 = -15 -4t = -15 Divide each side by '-4'. t = 3.75 Simplifying t = 3.75Solution
t = {0.75, 3.75}
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