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Simplifying (3a + -2b + 5c) + (7a + -3c) + (-2b + 7c) = 0 Remove parenthesis around (3a + -2b + 5c) 3a + -2b + 5c + (7a + -3c) + (-2b + 7c) = 0 Remove parenthesis around (7a + -3c) 3a + -2b + 5c + 7a + -3c + (-2b + 7c) = 0 Remove parenthesis around (-2b + 7c) 3a + -2b + 5c + 7a + -3c + -2b + 7c = 0 Reorder the terms: 3a + 7a + -2b + -2b + 5c + -3c + 7c = 0 Combine like terms: 3a + 7a = 10a 10a + -2b + -2b + 5c + -3c + 7c = 0 Combine like terms: -2b + -2b = -4b 10a + -4b + 5c + -3c + 7c = 0 Combine like terms: 5c + -3c = 2c 10a + -4b + 2c + 7c = 0 Combine like terms: 2c + 7c = 9c 10a + -4b + 9c = 0 Solving 10a + -4b + 9c = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '4b' to each side of the equation. 10a + -4b + 4b + 9c = 0 + 4b Combine like terms: -4b + 4b = 0 10a + 0 + 9c = 0 + 4b 10a + 9c = 0 + 4b Remove the zero: 10a + 9c = 4b Add '-9c' to each side of the equation. 10a + 9c + -9c = 4b + -9c Combine like terms: 9c + -9c = 0 10a + 0 = 4b + -9c 10a = 4b + -9c Divide each side by '10'. a = 0.4b + -0.9c Simplifying a = 0.4b + -0.9c
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