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Simplifying 12a + 19b + 2c + 5c + -6b + -2a = 0 Reorder the terms: 12a + -2a + 19b + -6b + 2c + 5c = 0 Combine like terms: 12a + -2a = 10a 10a + 19b + -6b + 2c + 5c = 0 Combine like terms: 19b + -6b = 13b 10a + 13b + 2c + 5c = 0 Combine like terms: 2c + 5c = 7c 10a + 13b + 7c = 0 Solving 10a + 13b + 7c = 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. 10a + 13b + -13b + 7c = 0 + -13b Combine like terms: 13b + -13b = 0 10a + 0 + 7c = 0 + -13b 10a + 7c = 0 + -13b Remove the zero: 10a + 7c = -13b Add '-7c' to each side of the equation. 10a + 7c + -7c = -13b + -7c Combine like terms: 7c + -7c = 0 10a + 0 = -13b + -7c 10a = -13b + -7c Divide each side by '10'. a = -1.3b + -0.7c Simplifying a = -1.3b + -0.7c
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