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Simplifying 10t2 = 2t3 + -72t Reorder the terms: 10t2 = -72t + 2t3 Solving 10t2 = -72t + 2t3 Solving for variable 't'. Reorder the terms: 72t + 10t2 + -2t3 = -72t + 2t3 + 72t + -2t3 Reorder the terms: 72t + 10t2 + -2t3 = -72t + 72t + 2t3 + -2t3 Combine like terms: -72t + 72t = 0 72t + 10t2 + -2t3 = 0 + 2t3 + -2t3 72t + 10t2 + -2t3 = 2t3 + -2t3 Combine like terms: 2t3 + -2t3 = 0 72t + 10t2 + -2t3 = 0 Factor out the Greatest Common Factor (GCF), '2t'. 2t(36 + 5t + -1t2) = 0 Factor a trinomial. 2t((9 + -1t)(4 + t)) = 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 '(9 + -1t)' equal to zero and attempt to solve: Simplifying 9 + -1t = 0 Solving 9 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -1t = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1t = 0 + -9 -1t = 0 + -9 Combine like terms: 0 + -9 = -9 -1t = -9 Divide each side by '-1'. t = 9 Simplifying t = 9Subproblem 3
Set the factor '(4 + t)' equal to zero and attempt to solve: Simplifying 4 + t = 0 Solving 4 + t = 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 + t = 0 + -4 Combine like terms: 4 + -4 = 0 0 + t = 0 + -4 t = 0 + -4 Combine like terms: 0 + -4 = -4 t = -4 Simplifying t = -4Solution
t = {0, 9, -4}
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