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Simplifying 6t + 3(5t + -4) = 12(2t + -2w) Reorder the terms: 6t + 3(-4 + 5t) = 12(2t + -2w) 6t + (-4 * 3 + 5t * 3) = 12(2t + -2w) 6t + (-12 + 15t) = 12(2t + -2w) Reorder the terms: -12 + 6t + 15t = 12(2t + -2w) Combine like terms: 6t + 15t = 21t -12 + 21t = 12(2t + -2w) -12 + 21t = (2t * 12 + -2w * 12) -12 + 21t = (24t + -24w) Solving -12 + 21t = 24t + -24w Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-24t' to each side of the equation. -12 + 21t + -24t = 24t + -24t + -24w Combine like terms: 21t + -24t = -3t -12 + -3t = 24t + -24t + -24w Combine like terms: 24t + -24t = 0 -12 + -3t = 0 + -24w -12 + -3t = -24w Add '12' to each side of the equation. -12 + 12 + -3t = 12 + -24w Combine like terms: -12 + 12 = 0 0 + -3t = 12 + -24w -3t = 12 + -24w Divide each side by '-3'. t = -4 + 8w Simplifying t = -4 + 8w
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