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Simplifying 15a + 19b + 6c + 5c + -6b + -3a = 0 Reorder the terms: 15a + -3a + 19b + -6b + 6c + 5c = 0 Combine like terms: 15a + -3a = 12a 12a + 19b + -6b + 6c + 5c = 0 Combine like terms: 19b + -6b = 13b 12a + 13b + 6c + 5c = 0 Combine like terms: 6c + 5c = 11c 12a + 13b + 11c = 0 Solving 12a + 13b + 11c = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-13b' to each side of the equation. 12a + 13b + -13b + 11c = 0 + -13b Combine like terms: 13b + -13b = 0 12a + 0 + 11c = 0 + -13b 12a + 11c = 0 + -13b Remove the zero: 12a + 11c = -13b Add '-11c' to each side of the equation. 12a + 11c + -11c = -13b + -11c Combine like terms: 11c + -11c = 0 12a + 0 = -13b + -11c 12a = -13b + -11c Divide each side by '12'. a = -1.083333333b + -0.9166666667c Simplifying a = -1.083333333b + -0.9166666667c
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