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Simplifying 7a(s + -4t) + 5b(s + -4t) + 3(s + -4t) = 0 (s * 7a + -4t * 7a) + 5b(s + -4t) + 3(s + -4t) = 0 (7as + -28at) + 5b(s + -4t) + 3(s + -4t) = 0 7as + -28at + (s * 5b + -4t * 5b) + 3(s + -4t) = 0 7as + -28at + (5bs + -20bt) + 3(s + -4t) = 0 7as + -28at + 5bs + -20bt + (s * 3 + -4t * 3) = 0 7as + -28at + 5bs + -20bt + (3s + -12t) = 0 Solving 7as + -28at + 5bs + -20bt + 3s + -12t = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-5bs' to each side of the equation. 7as + -28at + 5bs + -20bt + 3s + -5bs + -12t = 0 + -5bs Reorder the terms: 7as + -28at + 5bs + -5bs + -20bt + 3s + -12t = 0 + -5bs Combine like terms: 5bs + -5bs = 0 7as + -28at + 0 + -20bt + 3s + -12t = 0 + -5bs 7as + -28at + -20bt + 3s + -12t = 0 + -5bs Remove the zero: 7as + -28at + -20bt + 3s + -12t = -5bs Add '20bt' to each side of the equation. 7as + -28at + -20bt + 3s + 20bt + -12t = -5bs + 20bt Reorder the terms: 7as + -28at + -20bt + 20bt + 3s + -12t = -5bs + 20bt Combine like terms: -20bt + 20bt = 0 7as + -28at + 0 + 3s + -12t = -5bs + 20bt 7as + -28at + 3s + -12t = -5bs + 20bt Add '-3s' to each side of the equation. 7as + -28at + 3s + -3s + -12t = -5bs + 20bt + -3s Combine like terms: 3s + -3s = 0 7as + -28at + 0 + -12t = -5bs + 20bt + -3s 7as + -28at + -12t = -5bs + 20bt + -3s Add '12t' to each side of the equation. 7as + -28at + -12t + 12t = -5bs + 20bt + -3s + 12t Combine like terms: -12t + 12t = 0 7as + -28at + 0 = -5bs + 20bt + -3s + 12t 7as + -28at = -5bs + 20bt + -3s + 12t Reorder the terms: 7as + -28at + 5bs + -20bt + 3s + -12t = -5bs + 5bs + 20bt + -20bt + -3s + 3s + 12t + -12t Combine like terms: -5bs + 5bs = 0 7as + -28at + 5bs + -20bt + 3s + -12t = 0 + 20bt + -20bt + -3s + 3s + 12t + -12t 7as + -28at + 5bs + -20bt + 3s + -12t = 20bt + -20bt + -3s + 3s + 12t + -12t Combine like terms: 20bt + -20bt = 0 7as + -28at + 5bs + -20bt + 3s + -12t = 0 + -3s + 3s + 12t + -12t 7as + -28at + 5bs + -20bt + 3s + -12t = -3s + 3s + 12t + -12t Combine like terms: -3s + 3s = 0 7as + -28at + 5bs + -20bt + 3s + -12t = 0 + 12t + -12t 7as + -28at + 5bs + -20bt + 3s + -12t = 12t + -12t Combine like terms: 12t + -12t = 0 7as + -28at + 5bs + -20bt + 3s + -12t = 0 The solution to this equation could not be determined.
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