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Simplifying (2a + b + 3c) * 2 + (3a + 2b + -1c) * 2 = 0 Reorder the terms for easier multiplication: 2(2a + b + 3c) + (3a + 2b + -1c) * 2 = 0 (2a * 2 + b * 2 + 3c * 2) + (3a + 2b + -1c) * 2 = 0 (4a + 2b + 6c) + (3a + 2b + -1c) * 2 = 0 Reorder the terms for easier multiplication: 4a + 2b + 6c + 2(3a + 2b + -1c) = 0 4a + 2b + 6c + (3a * 2 + 2b * 2 + -1c * 2) = 0 4a + 2b + 6c + (6a + 4b + -2c) = 0 Reorder the terms: 4a + 6a + 2b + 4b + 6c + -2c = 0 Combine like terms: 4a + 6a = 10a 10a + 2b + 4b + 6c + -2c = 0 Combine like terms: 2b + 4b = 6b 10a + 6b + 6c + -2c = 0 Combine like terms: 6c + -2c = 4c 10a + 6b + 4c = 0 Solving 10a + 6b + 4c = 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. 10a + 6b + -6b + 4c = 0 + -6b Combine like terms: 6b + -6b = 0 10a + 0 + 4c = 0 + -6b 10a + 4c = 0 + -6b Remove the zero: 10a + 4c = -6b Add '-4c' to each side of the equation. 10a + 4c + -4c = -6b + -4c Combine like terms: 4c + -4c = 0 10a + 0 = -6b + -4c 10a = -6b + -4c Divide each side by '10'. a = -0.6b + -0.4c Simplifying a = -0.6b + -0.4c
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