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Simplifying 3t3 + 5t2 + 2t = 0 Reorder the terms: 2t + 5t2 + 3t3 = 0 Solving 2t + 5t2 + 3t3 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), 't'. t(2 + 5t + 3t2) = 0 Factor a trinomial. t((1 + t)(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 '(1 + t)' equal to zero and attempt to solve: Simplifying 1 + t = 0 Solving 1 + t = 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 + t = 0 + -1 Combine like terms: 1 + -1 = 0 0 + t = 0 + -1 t = 0 + -1 Combine like terms: 0 + -1 = -1 t = -1 Simplifying t = -1Subproblem 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, -1, -0.6666666667}
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