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Simplifying 0 = -16t2 + 42t + -20 Reorder the terms: 0 = -20 + 42t + -16t2 Solving 0 = -20 + 42t + -16t2 Solving for variable 't'. Combine like terms: 0 + 20 = 20 20 + -42t + 16t2 = -20 + 42t + -16t2 + 20 + -42t + 16t2 Reorder the terms: 20 + -42t + 16t2 = -20 + 20 + 42t + -42t + -16t2 + 16t2 Combine like terms: -20 + 20 = 0 20 + -42t + 16t2 = 0 + 42t + -42t + -16t2 + 16t2 20 + -42t + 16t2 = 42t + -42t + -16t2 + 16t2 Combine like terms: 42t + -42t = 0 20 + -42t + 16t2 = 0 + -16t2 + 16t2 20 + -42t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 20 + -42t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(10 + -21t + 8t2) = 0 Factor a trinomial. 2((5 + -8t)(2 + -1t)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(5 + -8t)' equal to zero and attempt to solve: Simplifying 5 + -8t = 0 Solving 5 + -8t = 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 + -8t = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -8t = 0 + -5 -8t = 0 + -5 Combine like terms: 0 + -5 = -5 -8t = -5 Divide each side by '-8'. t = 0.625 Simplifying t = 0.625Subproblem 2
Set the factor '(2 + -1t)' equal to zero and attempt to solve: Simplifying 2 + -1t = 0 Solving 2 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1t = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1t = 0 + -2 -1t = 0 + -2 Combine like terms: 0 + -2 = -2 -1t = -2 Divide each side by '-1'. t = 2 Simplifying t = 2Solution
t = {0.625, 2}
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