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Simplifying 40t = 60t(t + -1) Reorder the terms: 40t = 60t(-1 + t) 40t = (-1 * 60t + t * 60t) 40t = (-60t + 60t2) Solving 40t = -60t + 60t2 Solving for variable 't'. Combine like terms: 40t + 60t = 100t 100t + -60t2 = -60t + 60t2 + 60t + -60t2 Reorder the terms: 100t + -60t2 = -60t + 60t + 60t2 + -60t2 Combine like terms: -60t + 60t = 0 100t + -60t2 = 0 + 60t2 + -60t2 100t + -60t2 = 60t2 + -60t2 Combine like terms: 60t2 + -60t2 = 0 100t + -60t2 = 0 Factor out the Greatest Common Factor (GCF), '20t'. 20t(5 + -3t) = 0 Ignore the factor 20.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 '(5 + -3t)' equal to zero and attempt to solve: Simplifying 5 + -3t = 0 Solving 5 + -3t = 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 + -3t = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -3t = 0 + -5 -3t = 0 + -5 Combine like terms: 0 + -5 = -5 -3t = -5 Divide each side by '-3'. t = 1.666666667 Simplifying t = 1.666666667Solution
t = {0, 1.666666667}
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