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Simplifying 4(2a + b + -3c) = 0 (2a * 4 + b * 4 + -3c * 4) = 0 (8a + 4b + -12c) = 0 Solving 8a + 4b + -12c = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-4b' to each side of the equation. 8a + 4b + -4b + -12c = 0 + -4b Combine like terms: 4b + -4b = 0 8a + 0 + -12c = 0 + -4b 8a + -12c = 0 + -4b Remove the zero: 8a + -12c = -4b Add '12c' to each side of the equation. 8a + -12c + 12c = -4b + 12c Combine like terms: -12c + 12c = 0 8a + 0 = -4b + 12c 8a = -4b + 12c Divide each side by '8'. a = -0.5b + 1.5c Simplifying a = -0.5b + 1.5c
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