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Simplifying 2t3 + 9t2 + 10t = 0 Reorder the terms: 10t + 9t2 + 2t3 = 0 Solving 10t + 9t2 + 2t3 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), 't'. t(10 + 9t + 2t2) = 0 Factor a trinomial. t((5 + 2t)(2 + t)) = 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 '(5 + 2t)' equal to zero and attempt to solve: Simplifying 5 + 2t = 0 Solving 5 + 2t = 0 Move all terms containing t to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + 2t = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 2t = 0 + -5 2t = 0 + -5 Combine like terms: 0 + -5 = -5 2t = -5 Divide each side by '2'. t = -2.5 Simplifying t = -2.5Subproblem 3
Set the factor '(2 + t)' equal to zero and attempt to solve: Simplifying 2 + t = 0 Solving 2 + t = 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 + t = 0 + -2 Combine like terms: 2 + -2 = 0 0 + t = 0 + -2 t = 0 + -2 Combine like terms: 0 + -2 = -2 t = -2 Simplifying t = -2Solution
t = {0, -2.5, -2}
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