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Simplifying 9t3 + 30t2 + -24t = 0 Reorder the terms: -24t + 30t2 + 9t3 = 0 Solving -24t + 30t2 + 9t3 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '3t'. 3t(-8 + 10t + 3t2) = 0 Factor a trinomial. 3t((-4 + -1t)(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 '(-4 + -1t)' equal to zero and attempt to solve: Simplifying -4 + -1t = 0 Solving -4 + -1t = 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 + -1t = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1t = 0 + 4 -1t = 0 + 4 Combine like terms: 0 + 4 = 4 -1t = 4 Divide each side by '-1'. t = -4 Simplifying t = -4Subproblem 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, -4, 0.6666666667}
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