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Simplifying 0 = -8t(2t + -3) Reorder the terms: 0 = -8t(-3 + 2t) 0 = (-3 * -8t + 2t * -8t) 0 = (24t + -16t2) Solving 0 = 24t + -16t2 Solving for variable 't'. Remove the zero: -24t + 16t2 = 24t + -16t2 + -24t + 16t2 Reorder the terms: -24t + 16t2 = 24t + -24t + -16t2 + 16t2 Combine like terms: 24t + -24t = 0 -24t + 16t2 = 0 + -16t2 + 16t2 -24t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -24t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '8t'. 8t(-3 + 2t) = 0 Ignore the factor 8.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 '(-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 = {0, 1.5}
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