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Simplifying 0 = 4t3 + -42t2 + 90t Reorder the terms: 0 = 90t + -42t2 + 4t3 Solving 0 = 90t + -42t2 + 4t3 Solving for variable 't'. Remove the zero: -90t + 42t2 + -4t3 = 90t + -42t2 + 4t3 + -90t + 42t2 + -4t3 Reorder the terms: -90t + 42t2 + -4t3 = 90t + -90t + -42t2 + 42t2 + 4t3 + -4t3 Combine like terms: 90t + -90t = 0 -90t + 42t2 + -4t3 = 0 + -42t2 + 42t2 + 4t3 + -4t3 -90t + 42t2 + -4t3 = -42t2 + 42t2 + 4t3 + -4t3 Combine like terms: -42t2 + 42t2 = 0 -90t + 42t2 + -4t3 = 0 + 4t3 + -4t3 -90t + 42t2 + -4t3 = 4t3 + -4t3 Combine like terms: 4t3 + -4t3 = 0 -90t + 42t2 + -4t3 = 0 Factor out the Greatest Common Factor (GCF), '2t'. 2t(-45 + 21t + -2t2) = 0 Factor a trinomial. 2t((-15 + 2t)(3 + -1t)) = 0 Ignore the factor 2.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 '(-15 + 2t)' equal to zero and attempt to solve: Simplifying -15 + 2t = 0 Solving -15 + 2t = 0 Move all terms containing t to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + 2t = 0 + 15 Combine like terms: -15 + 15 = 0 0 + 2t = 0 + 15 2t = 0 + 15 Combine like terms: 0 + 15 = 15 2t = 15 Divide each side by '2'. t = 7.5 Simplifying t = 7.5Subproblem 3
Set the factor '(3 + -1t)' equal to zero and attempt to solve: Simplifying 3 + -1t = 0 Solving 3 + -1t = 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 + -1t = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1t = 0 + -3 -1t = 0 + -3 Combine like terms: 0 + -3 = -3 -1t = -3 Divide each side by '-1'. t = 3 Simplifying t = 3Solution
t = {0, 7.5, 3}
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