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Simplifying 6t3 + 13t2 = 5t Reorder the terms: 13t2 + 6t3 = 5t Solving 13t2 + 6t3 = 5t Solving for variable 't'. Reorder the terms: -5t + 13t2 + 6t3 = 5t + -5t Combine like terms: 5t + -5t = 0 -5t + 13t2 + 6t3 = 0 Factor out the Greatest Common Factor (GCF), 't'. t(-5 + 13t + 6t2) = 0 Factor a trinomial. t((-5 + -2t)(1 + -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 '(-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 '(1 + -3t)' equal to zero and attempt to solve: Simplifying 1 + -3t = 0 Solving 1 + -3t = 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 + -3t = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -3t = 0 + -1 -3t = 0 + -1 Combine like terms: 0 + -1 = -1 -3t = -1 Divide each side by '-3'. t = 0.3333333333 Simplifying t = 0.3333333333Solution
t = {0, -2.5, 0.3333333333}
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