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Simplifying -2t3 = 108t + -30t2 Solving -2t3 = 108t + -30t2 Solving for variable 't'. Reorder the terms: -108t + 30t2 + -2t3 = 108t + -30t2 + -108t + 30t2 Reorder the terms: -108t + 30t2 + -2t3 = 108t + -108t + -30t2 + 30t2 Combine like terms: 108t + -108t = 0 -108t + 30t2 + -2t3 = 0 + -30t2 + 30t2 -108t + 30t2 + -2t3 = -30t2 + 30t2 Combine like terms: -30t2 + 30t2 = 0 -108t + 30t2 + -2t3 = 0 Factor out the Greatest Common Factor (GCF), '2t'. 2t(-54 + 15t + -1t2) = 0 Factor a trinomial. 2t((-9 + t)(6 + -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 '(-9 + t)' equal to zero and attempt to solve: Simplifying -9 + t = 0 Solving -9 + t = 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 + t = 0 + 9 Combine like terms: -9 + 9 = 0 0 + t = 0 + 9 t = 0 + 9 Combine like terms: 0 + 9 = 9 t = 9 Simplifying t = 9Subproblem 3
Set the factor '(6 + -1t)' equal to zero and attempt to solve: Simplifying 6 + -1t = 0 Solving 6 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1t = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1t = 0 + -6 -1t = 0 + -6 Combine like terms: 0 + -6 = -6 -1t = -6 Divide each side by '-1'. t = 6 Simplifying t = 6Solution
t = {0, 9, 6}
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