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Simplifying 3t3 + 5t = -8t2 Reorder the terms: 5t + 3t3 = -8t2 Solving 5t + 3t3 = -8t2 Solving for variable 't'. Reorder the terms: 5t + 8t2 + 3t3 = -8t2 + 8t2 Combine like terms: -8t2 + 8t2 = 0 5t + 8t2 + 3t3 = 0 Factor out the Greatest Common Factor (GCF), 't'. t(5 + 8t + 3t2) = 0 Factor a trinomial. t((5 + 3t)(1 + 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 + 3t)' equal to zero and attempt to solve: Simplifying 5 + 3t = 0 Solving 5 + 3t = 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 + 3t = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 3t = 0 + -5 3t = 0 + -5 Combine like terms: 0 + -5 = -5 3t = -5 Divide each side by '3'. t = -1.666666667 Simplifying t = -1.666666667Subproblem 3
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 = -1Solution
t = {0, -1.666666667, -1}
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