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Simplifying 15a + 12b + 3c + 4c + -5b + -5a = 0 Reorder the terms: 15a + -5a + 12b + -5b + 3c + 4c = 0 Combine like terms: 15a + -5a = 10a 10a + 12b + -5b + 3c + 4c = 0 Combine like terms: 12b + -5b = 7b 10a + 7b + 3c + 4c = 0 Combine like terms: 3c + 4c = 7c 10a + 7b + 7c = 0 Solving 10a + 7b + 7c = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-7b' to each side of the equation. 10a + 7b + -7b + 7c = 0 + -7b Combine like terms: 7b + -7b = 0 10a + 0 + 7c = 0 + -7b 10a + 7c = 0 + -7b Remove the zero: 10a + 7c = -7b Add '-7c' to each side of the equation. 10a + 7c + -7c = -7b + -7c Combine like terms: 7c + -7c = 0 10a + 0 = -7b + -7c 10a = -7b + -7c Divide each side by '10'. a = -0.7b + -0.7c Simplifying a = -0.7b + -0.7c
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