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Simplifying 3(6a + -4b + 2c) + -2(1.5a + -1c) + -3(-1b + c) = 0 (6a * 3 + -4b * 3 + 2c * 3) + -2(1.5a + -1c) + -3(-1b + c) = 0 (18a + -12b + 6c) + -2(1.5a + -1c) + -3(-1b + c) = 0 18a + -12b + 6c + (1.5a * -2 + -1c * -2) + -3(-1b + c) = 0 18a + -12b + 6c + (-3a + 2c) + -3(-1b + c) = 0 18a + -12b + 6c + -3a + 2c + (-1b * -3 + c * -3) = 0 18a + -12b + 6c + -3a + 2c + (3b + -3c) = 0 Reorder the terms: 18a + -3a + -12b + 3b + 6c + 2c + -3c = 0 Combine like terms: 18a + -3a = 15a 15a + -12b + 3b + 6c + 2c + -3c = 0 Combine like terms: -12b + 3b = -9b 15a + -9b + 6c + 2c + -3c = 0 Combine like terms: 6c + 2c = 8c 15a + -9b + 8c + -3c = 0 Combine like terms: 8c + -3c = 5c 15a + -9b + 5c = 0 Solving 15a + -9b + 5c = 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. 15a + -9b + 9b + 5c = 0 + 9b Combine like terms: -9b + 9b = 0 15a + 0 + 5c = 0 + 9b 15a + 5c = 0 + 9b Remove the zero: 15a + 5c = 9b Add '-5c' to each side of the equation. 15a + 5c + -5c = 9b + -5c Combine like terms: 5c + -5c = 0 15a + 0 = 9b + -5c 15a = 9b + -5c Divide each side by '15'. a = 0.6b + -0.3333333333c Simplifying a = 0.6b + -0.3333333333c
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