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Simplifying 2(a + b + -3c) + -4(a + -1b + c) + 5a = 0 (a * 2 + b * 2 + -3c * 2) + -4(a + -1b + c) + 5a = 0 (2a + 2b + -6c) + -4(a + -1b + c) + 5a = 0 2a + 2b + -6c + (a * -4 + -1b * -4 + c * -4) + 5a = 0 2a + 2b + -6c + (-4a + 4b + -4c) + 5a = 0 Reorder the terms: 2a + -4a + 5a + 2b + 4b + -6c + -4c = 0 Combine like terms: 2a + -4a = -2a -2a + 5a + 2b + 4b + -6c + -4c = 0 Combine like terms: -2a + 5a = 3a 3a + 2b + 4b + -6c + -4c = 0 Combine like terms: 2b + 4b = 6b 3a + 6b + -6c + -4c = 0 Combine like terms: -6c + -4c = -10c 3a + 6b + -10c = 0 Solving 3a + 6b + -10c = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-6b' to each side of the equation. 3a + 6b + -6b + -10c = 0 + -6b Combine like terms: 6b + -6b = 0 3a + 0 + -10c = 0 + -6b 3a + -10c = 0 + -6b Remove the zero: 3a + -10c = -6b Add '10c' to each side of the equation. 3a + -10c + 10c = -6b + 10c Combine like terms: -10c + 10c = 0 3a + 0 = -6b + 10c 3a = -6b + 10c Divide each side by '3'. a = -2b + 3.333333333c Simplifying a = -2b + 3.333333333c
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