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Simplifying (a + 10b + -9) + (3a + -5b + 4c) + (2c + b + -6) = 0 Reorder the terms: (-9 + a + 10b) + (3a + -5b + 4c) + (2c + b + -6) = 0 Remove parenthesis around (-9 + a + 10b) -9 + a + 10b + (3a + -5b + 4c) + (2c + b + -6) = 0 Remove parenthesis around (3a + -5b + 4c) -9 + a + 10b + 3a + -5b + 4c + (2c + b + -6) = 0 Reorder the terms: -9 + a + 10b + 3a + -5b + 4c + (-6 + b + 2c) = 0 Remove parenthesis around (-6 + b + 2c) -9 + a + 10b + 3a + -5b + 4c + -6 + b + 2c = 0 Reorder the terms: -9 + -6 + a + 3a + 10b + -5b + b + 4c + 2c = 0 Combine like terms: -9 + -6 = -15 -15 + a + 3a + 10b + -5b + b + 4c + 2c = 0 Combine like terms: a + 3a = 4a -15 + 4a + 10b + -5b + b + 4c + 2c = 0 Combine like terms: 10b + -5b = 5b -15 + 4a + 5b + b + 4c + 2c = 0 Combine like terms: 5b + b = 6b -15 + 4a + 6b + 4c + 2c = 0 Combine like terms: 4c + 2c = 6c -15 + 4a + 6b + 6c = 0 Solving -15 + 4a + 6b + 6c = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 4a + 6b + 15 + 6c = 0 + 15 Reorder the terms: -15 + 15 + 4a + 6b + 6c = 0 + 15 Combine like terms: -15 + 15 = 0 0 + 4a + 6b + 6c = 0 + 15 4a + 6b + 6c = 0 + 15 Combine like terms: 0 + 15 = 15 4a + 6b + 6c = 15 Add '-6b' to each side of the equation. 4a + 6b + -6b + 6c = 15 + -6b Combine like terms: 6b + -6b = 0 4a + 0 + 6c = 15 + -6b 4a + 6c = 15 + -6b Add '-6c' to each side of the equation. 4a + 6c + -6c = 15 + -6b + -6c Combine like terms: 6c + -6c = 0 4a + 0 = 15 + -6b + -6c 4a = 15 + -6b + -6c Divide each side by '4'. a = 3.75 + -1.5b + -1.5c Simplifying a = 3.75 + -1.5b + -1.5c
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