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Simplifying 16t3 = 40t2 + -25t Reorder the terms: 16t3 = -25t + 40t2 Solving 16t3 = -25t + 40t2 Solving for variable 't'. Reorder the terms: 25t + -40t2 + 16t3 = -25t + 40t2 + 25t + -40t2 Reorder the terms: 25t + -40t2 + 16t3 = -25t + 25t + 40t2 + -40t2 Combine like terms: -25t + 25t = 0 25t + -40t2 + 16t3 = 0 + 40t2 + -40t2 25t + -40t2 + 16t3 = 40t2 + -40t2 Combine like terms: 40t2 + -40t2 = 0 25t + -40t2 + 16t3 = 0 Factor out the Greatest Common Factor (GCF), 't'. t(25 + -40t + 16t2) = 0 Factor a trinomial. t((5 + -4t)(5 + -4t)) = 0Subproblem 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 '(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 = 1.25Subproblem 3
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, 1.25, 1.25}
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