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Simplifying 3(2a + b + -3c) = 0 (2a * 3 + b * 3 + -3c * 3) = 0 (6a + 3b + -9c) = 0 Solving 6a + 3b + -9c = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-3b' to each side of the equation. 6a + 3b + -3b + -9c = 0 + -3b Combine like terms: 3b + -3b = 0 6a + 0 + -9c = 0 + -3b 6a + -9c = 0 + -3b Remove the zero: 6a + -9c = -3b Add '9c' to each side of the equation. 6a + -9c + 9c = -3b + 9c Combine like terms: -9c + 9c = 0 6a + 0 = -3b + 9c 6a = -3b + 9c Divide each side by '6'. a = -0.5b + 1.5c Simplifying a = -0.5b + 1.5c
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