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Simplifying 15a + -3b + 12c + -5a + b + -10c = 0 Reorder the terms: 15a + -5a + -3b + b + 12c + -10c = 0 Combine like terms: 15a + -5a = 10a 10a + -3b + b + 12c + -10c = 0 Combine like terms: -3b + b = -2b 10a + -2b + 12c + -10c = 0 Combine like terms: 12c + -10c = 2c 10a + -2b + 2c = 0 Solving 10a + -2b + 2c = 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. 10a + -2b + 2b + 2c = 0 + 2b Combine like terms: -2b + 2b = 0 10a + 0 + 2c = 0 + 2b 10a + 2c = 0 + 2b Remove the zero: 10a + 2c = 2b Add '-2c' to each side of the equation. 10a + 2c + -2c = 2b + -2c Combine like terms: 2c + -2c = 0 10a + 0 = 2b + -2c 10a = 2b + -2c Divide each side by '10'. a = 0.2b + -0.2c Simplifying a = 0.2b + -0.2c
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