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Simplifying 8(4a + -1b) + -4(3b + -4a) = 0 (4a * 8 + -1b * 8) + -4(3b + -4a) = 0 (32a + -8b) + -4(3b + -4a) = 0 Reorder the terms: 32a + -8b + -4(-4a + 3b) = 0 32a + -8b + (-4a * -4 + 3b * -4) = 0 32a + -8b + (16a + -12b) = 0 Reorder the terms: 32a + 16a + -8b + -12b = 0 Combine like terms: 32a + 16a = 48a 48a + -8b + -12b = 0 Combine like terms: -8b + -12b = -20b 48a + -20b = 0 Solving 48a + -20b = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '20b' to each side of the equation. 48a + -20b + 20b = 0 + 20b Combine like terms: -20b + 20b = 0 48a + 0 = 0 + 20b 48a = 0 + 20b Remove the zero: 48a = 20b Divide each side by '48'. a = 0.4166666667b Simplifying a = 0.4166666667b
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