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Simplifying 12a + 13b + 3c + 3c + -4b + -2a = 0 Reorder the terms: 12a + -2a + 13b + -4b + 3c + 3c = 0 Combine like terms: 12a + -2a = 10a 10a + 13b + -4b + 3c + 3c = 0 Combine like terms: 13b + -4b = 9b 10a + 9b + 3c + 3c = 0 Combine like terms: 3c + 3c = 6c 10a + 9b + 6c = 0 Solving 10a + 9b + 6c = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-9b' to each side of the equation. 10a + 9b + -9b + 6c = 0 + -9b Combine like terms: 9b + -9b = 0 10a + 0 + 6c = 0 + -9b 10a + 6c = 0 + -9b Remove the zero: 10a + 6c = -9b Add '-6c' to each side of the equation. 10a + 6c + -6c = -9b + -6c Combine like terms: 6c + -6c = 0 10a + 0 = -9b + -6c 10a = -9b + -6c Divide each side by '10'. a = -0.9b + -0.6c Simplifying a = -0.9b + -0.6c
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