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Simplifying 0 = 9t2 + 6t + -27t3 Reorder the terms: 0 = 6t + 9t2 + -27t3 Solving 0 = 6t + 9t2 + -27t3 Solving for variable 't'. Remove the zero: -6t + -9t2 + 27t3 = 6t + 9t2 + -27t3 + -6t + -9t2 + 27t3 Reorder the terms: -6t + -9t2 + 27t3 = 6t + -6t + 9t2 + -9t2 + -27t3 + 27t3 Combine like terms: 6t + -6t = 0 -6t + -9t2 + 27t3 = 0 + 9t2 + -9t2 + -27t3 + 27t3 -6t + -9t2 + 27t3 = 9t2 + -9t2 + -27t3 + 27t3 Combine like terms: 9t2 + -9t2 = 0 -6t + -9t2 + 27t3 = 0 + -27t3 + 27t3 -6t + -9t2 + 27t3 = -27t3 + 27t3 Combine like terms: -27t3 + 27t3 = 0 -6t + -9t2 + 27t3 = 0 Factor out the Greatest Common Factor (GCF), '3t'. 3t(-2 + -3t + 9t2) = 0 Factor a trinomial. 3t((-1 + -3t)(2 + -3t)) = 0 Ignore the factor 3.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 '(-1 + -3t)' equal to zero and attempt to solve: Simplifying -1 + -3t = 0 Solving -1 + -3t = 0 Move all terms containing t to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -3t = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -3t = 0 + 1 -3t = 0 + 1 Combine like terms: 0 + 1 = 1 -3t = 1 Divide each side by '-3'. t = -0.3333333333 Simplifying t = -0.3333333333Subproblem 3
Set the factor '(2 + -3t)' equal to zero and attempt to solve: Simplifying 2 + -3t = 0 Solving 2 + -3t = 0 Move all terms containing t to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -3t = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3t = 0 + -2 -3t = 0 + -2 Combine like terms: 0 + -2 = -2 -3t = -2 Divide each side by '-3'. t = 0.6666666667 Simplifying t = 0.6666666667Solution
t = {0, -0.3333333333, 0.6666666667}
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