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Simplifying (7a + 4b + -7c) + (5a + -7b + -10c) = 0 Remove parenthesis around (7a + 4b + -7c) 7a + 4b + -7c + (5a + -7b + -10c) = 0 Remove parenthesis around (5a + -7b + -10c) 7a + 4b + -7c + 5a + -7b + -10c = 0 Reorder the terms: 7a + 5a + 4b + -7b + -7c + -10c = 0 Combine like terms: 7a + 5a = 12a 12a + 4b + -7b + -7c + -10c = 0 Combine like terms: 4b + -7b = -3b 12a + -3b + -7c + -10c = 0 Combine like terms: -7c + -10c = -17c 12a + -3b + -17c = 0 Solving 12a + -3b + -17c = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '3b' to each side of the equation. 12a + -3b + 3b + -17c = 0 + 3b Combine like terms: -3b + 3b = 0 12a + 0 + -17c = 0 + 3b 12a + -17c = 0 + 3b Remove the zero: 12a + -17c = 3b Add '17c' to each side of the equation. 12a + -17c + 17c = 3b + 17c Combine like terms: -17c + 17c = 0 12a + 0 = 3b + 17c 12a = 3b + 17c Divide each side by '12'. a = 0.25b + 1.416666667c Simplifying a = 0.25b + 1.416666667c
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