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Simplifying 6t2 = 13t + 5 Reorder the terms: 6t2 = 5 + 13t Solving 6t2 = 5 + 13t Solving for variable 't'. Reorder the terms: -5 + -13t + 6t2 = 5 + 13t + -5 + -13t Reorder the terms: -5 + -13t + 6t2 = 5 + -5 + 13t + -13t Combine like terms: 5 + -5 = 0 -5 + -13t + 6t2 = 0 + 13t + -13t -5 + -13t + 6t2 = 13t + -13t Combine like terms: 13t + -13t = 0 -5 + -13t + 6t2 = 0 Factor a trinomial. (-1 + -3t)(5 + -2t) = 0Subproblem 1
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 = -0.3333333333Subproblem 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 = 2.5Solution
t = {-0.3333333333, 2.5}
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