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Simplifying -5t3 = 100t + -45t2 Solving -5t3 = 100t + -45t2 Solving for variable 't'. Reorder the terms: -100t + 45t2 + -5t3 = 100t + -45t2 + -100t + 45t2 Reorder the terms: -100t + 45t2 + -5t3 = 100t + -100t + -45t2 + 45t2 Combine like terms: 100t + -100t = 0 -100t + 45t2 + -5t3 = 0 + -45t2 + 45t2 -100t + 45t2 + -5t3 = -45t2 + 45t2 Combine like terms: -45t2 + 45t2 = 0 -100t + 45t2 + -5t3 = 0 Factor out the Greatest Common Factor (GCF), '5t'. 5t(-20 + 9t + -1t2) = 0 Factor a trinomial. 5t((-5 + t)(4 + -1t)) = 0 Ignore the factor 5.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 + t)' equal to zero and attempt to solve: Simplifying -5 + t = 0 Solving -5 + t = 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 + t = 0 + 5 Combine like terms: -5 + 5 = 0 0 + t = 0 + 5 t = 0 + 5 Combine like terms: 0 + 5 = 5 t = 5 Simplifying t = 5Subproblem 3
Set the factor '(4 + -1t)' equal to zero and attempt to solve: Simplifying 4 + -1t = 0 Solving 4 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1t = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1t = 0 + -4 -1t = 0 + -4 Combine like terms: 0 + -4 = -4 -1t = -4 Divide each side by '-1'. t = 4 Simplifying t = 4Solution
t = {0, 5, 4}
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