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Simplifying (2a + -3b + -5c) + (3a + 4b + 7c) = 0 Remove parenthesis around (2a + -3b + -5c) 2a + -3b + -5c + (3a + 4b + 7c) = 0 Remove parenthesis around (3a + 4b + 7c) 2a + -3b + -5c + 3a + 4b + 7c = 0 Reorder the terms: 2a + 3a + -3b + 4b + -5c + 7c = 0 Combine like terms: 2a + 3a = 5a 5a + -3b + 4b + -5c + 7c = 0 Combine like terms: -3b + 4b = 1b 5a + 1b + -5c + 7c = 0 Combine like terms: -5c + 7c = 2c 5a + 1b + 2c = 0 Solving 5a + 1b + 2c = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1b' to each side of the equation. 5a + 1b + -1b + 2c = 0 + -1b Combine like terms: 1b + -1b = 0 5a + 0 + 2c = 0 + -1b 5a + 2c = 0 + -1b Remove the zero: 5a + 2c = -1b Add '-2c' to each side of the equation. 5a + 2c + -2c = -1b + -2c Combine like terms: 2c + -2c = 0 5a + 0 = -1b + -2c 5a = -1b + -2c Divide each side by '5'. a = -0.2b + -0.4c Simplifying a = -0.2b + -0.4c
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