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Simplifying 3b + 5a + -4c + -5b + 7a = 0 Reorder the terms: 5a + 7a + 3b + -5b + -4c = 0 Combine like terms: 5a + 7a = 12a 12a + 3b + -5b + -4c = 0 Combine like terms: 3b + -5b = -2b 12a + -2b + -4c = 0 Solving 12a + -2b + -4c = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '2b' to each side of the equation. 12a + -2b + 2b + -4c = 0 + 2b Combine like terms: -2b + 2b = 0 12a + 0 + -4c = 0 + 2b 12a + -4c = 0 + 2b Remove the zero: 12a + -4c = 2b Add '4c' to each side of the equation. 12a + -4c + 4c = 2b + 4c Combine like terms: -4c + 4c = 0 12a + 0 = 2b + 4c 12a = 2b + 4c Divide each side by '12'. a = 0.1666666667b + 0.3333333333c Simplifying a = 0.1666666667b + 0.3333333333c
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