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Simplifying 6(2a + -3c) + 3(1 + d) = 0 (2a * 6 + -3c * 6) + 3(1 + d) = 0 (12a + -18c) + 3(1 + d) = 0 12a + -18c + (1 * 3 + d * 3) = 0 12a + -18c + (3 + 3d) = 0 Reorder the terms: 3 + 12a + -18c + 3d = 0 Solving 3 + 12a + -18c + 3d = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + 12a + -18c + -3 + 3d = 0 + -3 Reorder the terms: 3 + -3 + 12a + -18c + 3d = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 12a + -18c + 3d = 0 + -3 12a + -18c + 3d = 0 + -3 Combine like terms: 0 + -3 = -3 12a + -18c + 3d = -3 Add '18c' to each side of the equation. 12a + -18c + 18c + 3d = -3 + 18c Combine like terms: -18c + 18c = 0 12a + 0 + 3d = -3 + 18c 12a + 3d = -3 + 18c Add '-3d' to each side of the equation. 12a + 3d + -3d = -3 + 18c + -3d Combine like terms: 3d + -3d = 0 12a + 0 = -3 + 18c + -3d 12a = -3 + 18c + -3d Divide each side by '12'. a = -0.25 + 1.5c + -0.25d Simplifying a = -0.25 + 1.5c + -0.25d
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