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Simplifying 0 = 2t(-8t + 23) Reorder the terms: 0 = 2t(23 + -8t) 0 = (23 * 2t + -8t * 2t) 0 = (46t + -16t2) Solving 0 = 46t + -16t2 Solving for variable 't'. Remove the zero: -46t + 16t2 = 46t + -16t2 + -46t + 16t2 Reorder the terms: -46t + 16t2 = 46t + -46t + -16t2 + 16t2 Combine like terms: 46t + -46t = 0 -46t + 16t2 = 0 + -16t2 + 16t2 -46t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -46t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2t'. 2t(-23 + 8t) = 0 Ignore the factor 2.Subproblem 1
Set the factor 't' equal to zero and attempt to solve: Simplifying t = 0 Solving t = 0 Move all terms containing t to the left, all other terms to the right. Simplifying t = 0Subproblem 2
Set the factor '(-23 + 8t)' equal to zero and attempt to solve: Simplifying -23 + 8t = 0 Solving -23 + 8t = 0 Move all terms containing t to the left, all other terms to the right. Add '23' to each side of the equation. -23 + 23 + 8t = 0 + 23 Combine like terms: -23 + 23 = 0 0 + 8t = 0 + 23 8t = 0 + 23 Combine like terms: 0 + 23 = 23 8t = 23 Divide each side by '8'. t = 2.875 Simplifying t = 2.875Solution
t = {0, 2.875}
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