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Simplifying 12(t + -3) * 5 = 2(3t + 4) * 3 Reorder the terms: 12(-3 + t) * 5 = 2(3t + 4) * 3 Reorder the terms for easier multiplication: 12 * 5(-3 + t) = 2(3t + 4) * 3 Multiply 12 * 5 60(-3 + t) = 2(3t + 4) * 3 (-3 * 60 + t * 60) = 2(3t + 4) * 3 (-180 + 60t) = 2(3t + 4) * 3 Reorder the terms: -180 + 60t = 2(4 + 3t) * 3 Reorder the terms for easier multiplication: -180 + 60t = 2 * 3(4 + 3t) Multiply 2 * 3 -180 + 60t = 6(4 + 3t) -180 + 60t = (4 * 6 + 3t * 6) -180 + 60t = (24 + 18t) Solving -180 + 60t = 24 + 18t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-18t' to each side of the equation. -180 + 60t + -18t = 24 + 18t + -18t Combine like terms: 60t + -18t = 42t -180 + 42t = 24 + 18t + -18t Combine like terms: 18t + -18t = 0 -180 + 42t = 24 + 0 -180 + 42t = 24 Add '180' to each side of the equation. -180 + 180 + 42t = 24 + 180 Combine like terms: -180 + 180 = 0 0 + 42t = 24 + 180 42t = 24 + 180 Combine like terms: 24 + 180 = 204 42t = 204 Divide each side by '42'. t = 4.857142857 Simplifying t = 4.857142857
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