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Simplifying (5a + 3b + -6c) + (2a + 4b + 13c) = 0 Remove parenthesis around (5a + 3b + -6c) 5a + 3b + -6c + (2a + 4b + 13c) = 0 Remove parenthesis around (2a + 4b + 13c) 5a + 3b + -6c + 2a + 4b + 13c = 0 Reorder the terms: 5a + 2a + 3b + 4b + -6c + 13c = 0 Combine like terms: 5a + 2a = 7a 7a + 3b + 4b + -6c + 13c = 0 Combine like terms: 3b + 4b = 7b 7a + 7b + -6c + 13c = 0 Combine like terms: -6c + 13c = 7c 7a + 7b + 7c = 0 Solving 7a + 7b + 7c = 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 + 7c = 0 + -7b Combine like terms: 7b + -7b = 0 7a + 0 + 7c = 0 + -7b 7a + 7c = 0 + -7b Remove the zero: 7a + 7c = -7b Add '-7c' to each side of the equation. 7a + 7c + -7c = -7b + -7c Combine like terms: 7c + -7c = 0 7a + 0 = -7b + -7c 7a = -7b + -7c Divide each side by '7'. a = -1b + -1c Simplifying a = -1b + -1c
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