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Simplifying -9t3 + 12t2 + -4t = 0 Reorder the terms: -4t + 12t2 + -9t3 = 0 Solving -4t + 12t2 + -9t3 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), 't'. t(-4 + 12t + -9t2) = 0 Factor a trinomial. t((-2 + 3t)(2 + -3t)) = 0Subproblem 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 '(-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 = 0.6666666667Subproblem 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, 0.6666666667, 0.6666666667}
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