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Simplifying 12(8t + 1) = 6(t + 8) + 6(t + -6) Reorder the terms: 12(1 + 8t) = 6(t + 8) + 6(t + -6) (1 * 12 + 8t * 12) = 6(t + 8) + 6(t + -6) (12 + 96t) = 6(t + 8) + 6(t + -6) Reorder the terms: 12 + 96t = 6(8 + t) + 6(t + -6) 12 + 96t = (8 * 6 + t * 6) + 6(t + -6) 12 + 96t = (48 + 6t) + 6(t + -6) Reorder the terms: 12 + 96t = 48 + 6t + 6(-6 + t) 12 + 96t = 48 + 6t + (-6 * 6 + t * 6) 12 + 96t = 48 + 6t + (-36 + 6t) Reorder the terms: 12 + 96t = 48 + -36 + 6t + 6t Combine like terms: 48 + -36 = 12 12 + 96t = 12 + 6t + 6t Combine like terms: 6t + 6t = 12t 12 + 96t = 12 + 12t Add '-12' to each side of the equation. 12 + -12 + 96t = 12 + -12 + 12t Combine like terms: 12 + -12 = 0 0 + 96t = 12 + -12 + 12t 96t = 12 + -12 + 12t Combine like terms: 12 + -12 = 0 96t = 0 + 12t 96t = 12t Solving 96t = 12t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-12t' to each side of the equation. 96t + -12t = 12t + -12t Combine like terms: 96t + -12t = 84t 84t = 12t + -12t Combine like terms: 12t + -12t = 0 84t = 0 Divide each side by '84'. t = 0 Simplifying t = 0
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