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Simplifying (t * 6) + ((t + -30) * 6) = 600 Reorder the terms for easier multiplication: (6t) + ((t + -30) * 6) = 600 Reorder the terms: (6t) + ((-30 + t) * 6) = 600 Reorder the terms for easier multiplication: (6t) + (6(-30 + t)) = 600 (6t) + ((-30 * 6 + t * 6)) = 600 (6t) + ((-180 + 6t)) = 600 (6t) + (-180 + 6t) = 600 Remove parenthesis around (-180 + 6t) (6t) + -180 + 6t = 600 Reorder the terms: -180 + (6t) + 6t = 600 Combine like terms: (6t) + 6t = 12t -180 + 12t = 600 Solving -180 + 12t = 600 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '180' to each side of the equation. -180 + 180 + 12t = 600 + 180 Combine like terms: -180 + 180 = 0 0 + 12t = 600 + 180 12t = 600 + 180 Combine like terms: 600 + 180 = 780 12t = 780 Divide each side by '12'. t = 65 Simplifying t = 65
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