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Simplifying 400t = -16t2 + 96t Reorder the terms: 400t = 96t + -16t2 Solving 400t = 96t + -16t2 Solving for variable 't'. Combine like terms: 400t + -96t = 304t 304t + 16t2 = 96t + -16t2 + -96t + 16t2 Reorder the terms: 304t + 16t2 = 96t + -96t + -16t2 + 16t2 Combine like terms: 96t + -96t = 0 304t + 16t2 = 0 + -16t2 + 16t2 304t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 304t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '16t'. 16t(19 + t) = 0 Ignore the factor 16.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 '(19 + t)' equal to zero and attempt to solve: Simplifying 19 + t = 0 Solving 19 + t = 0 Move all terms containing t to the left, all other terms to the right. Add '-19' to each side of the equation. 19 + -19 + t = 0 + -19 Combine like terms: 19 + -19 = 0 0 + t = 0 + -19 t = 0 + -19 Combine like terms: 0 + -19 = -19 t = -19 Simplifying t = -19Solution
t = {0, -19}
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