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Simplifying t(t + 5) + -1t(t + -8) = 3(t + -8) + -5(t + -5) Reorder the terms: t(5 + t) + -1t(t + -8) = 3(t + -8) + -5(t + -5) (5 * t + t * t) + -1t(t + -8) = 3(t + -8) + -5(t + -5) (5t + t2) + -1t(t + -8) = 3(t + -8) + -5(t + -5) Reorder the terms: 5t + t2 + -1t(-8 + t) = 3(t + -8) + -5(t + -5) 5t + t2 + (-8 * -1t + t * -1t) = 3(t + -8) + -5(t + -5) 5t + t2 + (8t + -1t2) = 3(t + -8) + -5(t + -5) Reorder the terms: 5t + 8t + t2 + -1t2 = 3(t + -8) + -5(t + -5) Combine like terms: 5t + 8t = 13t 13t + t2 + -1t2 = 3(t + -8) + -5(t + -5) Combine like terms: t2 + -1t2 = 0 13t + 0 = 3(t + -8) + -5(t + -5) 13t = 3(t + -8) + -5(t + -5) Reorder the terms: 13t = 3(-8 + t) + -5(t + -5) 13t = (-8 * 3 + t * 3) + -5(t + -5) 13t = (-24 + 3t) + -5(t + -5) Reorder the terms: 13t = -24 + 3t + -5(-5 + t) 13t = -24 + 3t + (-5 * -5 + t * -5) 13t = -24 + 3t + (25 + -5t) Reorder the terms: 13t = -24 + 25 + 3t + -5t Combine like terms: -24 + 25 = 1 13t = 1 + 3t + -5t Combine like terms: 3t + -5t = -2t 13t = 1 + -2t Solving 13t = 1 + -2t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2t' to each side of the equation. 13t + 2t = 1 + -2t + 2t Combine like terms: 13t + 2t = 15t 15t = 1 + -2t + 2t Combine like terms: -2t + 2t = 0 15t = 1 + 0 15t = 1 Divide each side by '15'. t = 0.06666666667 Simplifying t = 0.06666666667
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