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Simplifying 0 = -16t2 + 32t + -15 Reorder the terms: 0 = -15 + 32t + -16t2 Solving 0 = -15 + 32t + -16t2 Solving for variable 't'. Combine like terms: 0 + 15 = 15 15 + -32t + 16t2 = -15 + 32t + -16t2 + 15 + -32t + 16t2 Reorder the terms: 15 + -32t + 16t2 = -15 + 15 + 32t + -32t + -16t2 + 16t2 Combine like terms: -15 + 15 = 0 15 + -32t + 16t2 = 0 + 32t + -32t + -16t2 + 16t2 15 + -32t + 16t2 = 32t + -32t + -16t2 + 16t2 Combine like terms: 32t + -32t = 0 15 + -32t + 16t2 = 0 + -16t2 + 16t2 15 + -32t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 15 + -32t + 16t2 = 0 Factor a trinomial. (3 + -4t)(5 + -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 '(5 + -4t)' equal to zero and attempt to solve: Simplifying 5 + -4t = 0 Solving 5 + -4t = 0 Move all terms containing t to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -4t = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -4t = 0 + -5 -4t = 0 + -5 Combine like terms: 0 + -5 = -5 -4t = -5 Divide each side by '-4'. t = 1.25 Simplifying t = 1.25Solution
t = {0.75, 1.25}
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