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Simplifying 0 = 2t3 + -12t2 + 18t Reorder the terms: 0 = 18t + -12t2 + 2t3 Solving 0 = 18t + -12t2 + 2t3 Solving for variable 't'. Remove the zero: -18t + 12t2 + -2t3 = 18t + -12t2 + 2t3 + -18t + 12t2 + -2t3 Reorder the terms: -18t + 12t2 + -2t3 = 18t + -18t + -12t2 + 12t2 + 2t3 + -2t3 Combine like terms: 18t + -18t = 0 -18t + 12t2 + -2t3 = 0 + -12t2 + 12t2 + 2t3 + -2t3 -18t + 12t2 + -2t3 = -12t2 + 12t2 + 2t3 + -2t3 Combine like terms: -12t2 + 12t2 = 0 -18t + 12t2 + -2t3 = 0 + 2t3 + -2t3 -18t + 12t2 + -2t3 = 2t3 + -2t3 Combine like terms: 2t3 + -2t3 = 0 -18t + 12t2 + -2t3 = 0 Factor out the Greatest Common Factor (GCF), '2t'. 2t(-9 + 6t + -1t2) = 0 Factor a trinomial. 2t((-3 + t)(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 '(-3 + t)' equal to zero and attempt to solve: Simplifying -3 + t = 0 Solving -3 + t = 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 + t = 0 + 3 Combine like terms: -3 + 3 = 0 0 + t = 0 + 3 t = 0 + 3 Combine like terms: 0 + 3 = 3 t = 3 Simplifying t = 3Subproblem 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, 3, 3}
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