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Simplifying 6(9a + -3d) + -8(2a + 4b) = 0 (9a * 6 + -3d * 6) + -8(2a + 4b) = 0 (54a + -18d) + -8(2a + 4b) = 0 54a + -18d + (2a * -8 + 4b * -8) = 0 54a + -18d + (-16a + -32b) = 0 Reorder the terms: 54a + -16a + -32b + -18d = 0 Combine like terms: 54a + -16a = 38a 38a + -32b + -18d = 0 Solving 38a + -32b + -18d = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '32b' to each side of the equation. 38a + -32b + 32b + -18d = 0 + 32b Combine like terms: -32b + 32b = 0 38a + 0 + -18d = 0 + 32b 38a + -18d = 0 + 32b Remove the zero: 38a + -18d = 32b Add '18d' to each side of the equation. 38a + -18d + 18d = 32b + 18d Combine like terms: -18d + 18d = 0 38a + 0 = 32b + 18d 38a = 32b + 18d Divide each side by '38'. a = 0.8421052632b + 0.4736842105d Simplifying a = 0.8421052632b + 0.4736842105d
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