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Simplifying 3(a + -5c) + -4(b + -1a) + 3(c + -1b) = 0 (a * 3 + -5c * 3) + -4(b + -1a) + 3(c + -1b) = 0 (3a + -15c) + -4(b + -1a) + 3(c + -1b) = 0 Reorder the terms: 3a + -15c + -4(-1a + b) + 3(c + -1b) = 0 3a + -15c + (-1a * -4 + b * -4) + 3(c + -1b) = 0 3a + -15c + (4a + -4b) + 3(c + -1b) = 0 Reorder the terms: 3a + -15c + 4a + -4b + 3(-1b + c) = 0 3a + -15c + 4a + -4b + (-1b * 3 + c * 3) = 0 3a + -15c + 4a + -4b + (-3b + 3c) = 0 Reorder the terms: 3a + 4a + -4b + -3b + -15c + 3c = 0 Combine like terms: 3a + 4a = 7a 7a + -4b + -3b + -15c + 3c = 0 Combine like terms: -4b + -3b = -7b 7a + -7b + -15c + 3c = 0 Combine like terms: -15c + 3c = -12c 7a + -7b + -12c = 0 Solving 7a + -7b + -12c = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '7b' to each side of the equation. 7a + -7b + 7b + -12c = 0 + 7b Combine like terms: -7b + 7b = 0 7a + 0 + -12c = 0 + 7b 7a + -12c = 0 + 7b Remove the zero: 7a + -12c = 7b Add '12c' to each side of the equation. 7a + -12c + 12c = 7b + 12c Combine like terms: -12c + 12c = 0 7a + 0 = 7b + 12c 7a = 7b + 12c Divide each side by '7'. a = b + 1.714285714c Simplifying a = b + 1.714285714c
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