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Simplifying 6(6a + -1b) + -7(4b + -4a) = 0 (6a * 6 + -1b * 6) + -7(4b + -4a) = 0 (36a + -6b) + -7(4b + -4a) = 0 Reorder the terms: 36a + -6b + -7(-4a + 4b) = 0 36a + -6b + (-4a * -7 + 4b * -7) = 0 36a + -6b + (28a + -28b) = 0 Reorder the terms: 36a + 28a + -6b + -28b = 0 Combine like terms: 36a + 28a = 64a 64a + -6b + -28b = 0 Combine like terms: -6b + -28b = -34b 64a + -34b = 0 Solving 64a + -34b = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '34b' to each side of the equation. 64a + -34b + 34b = 0 + 34b Combine like terms: -34b + 34b = 0 64a + 0 = 0 + 34b 64a = 0 + 34b Remove the zero: 64a = 34b Divide each side by '64'. a = 0.53125b Simplifying a = 0.53125b
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