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Simplifying 4t + -2(3 + -1t) + -3(t + -7) = 0 4t + (3 * -2 + -1t * -2) + -3(t + -7) = 0 4t + (-6 + 2t) + -3(t + -7) = 0 Reorder the terms: 4t + -6 + 2t + -3(-7 + t) = 0 4t + -6 + 2t + (-7 * -3 + t * -3) = 0 4t + -6 + 2t + (21 + -3t) = 0 Reorder the terms: -6 + 21 + 4t + 2t + -3t = 0 Combine like terms: -6 + 21 = 15 15 + 4t + 2t + -3t = 0 Combine like terms: 4t + 2t = 6t 15 + 6t + -3t = 0 Combine like terms: 6t + -3t = 3t 15 + 3t = 0 Solving 15 + 3t = 0 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + 3t = 0 + -15 Combine like terms: 15 + -15 = 0 0 + 3t = 0 + -15 3t = 0 + -15 Combine like terms: 0 + -15 = -15 3t = -15 Divide each side by '3'. t = -5 Simplifying t = -5
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